Results of Numerical Methods: Difference between revisions

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{| class="wikitable sortable" style="margin: 0;"
; Areas : [[3.1|3.1 Arithmetics and Error Measures]]<br>[[3.2|3.2 Linear Algebra]]<br>[[3.3|3.3 Interpolation]]<br>[[3.4|3.4 Differentiation]]<br>[[3.5|3.5 Quadrature]]<br>[[3.6|3.6 Linear Difference Equations]]<br>[[3.7|3.7 Ordinary Differential Equations]]<br>[[3.8|3.8 Nonlinear Equations]]<br>[[3.9|3.9 Acceleration of Convergence]]<br>[[3.10|3.10 Continued Fractions]]<br>[[3.11|3.11 Approximation Techniques]]<br>[[3.12|3.12 Mathematical Constants]]<br>
|-
! scope="col" style="position: sticky; top: 0;" | DLMF
! scope="col" style="position: sticky; top: 0;" | Formula
! scope="col" style="position: sticky; top: 0;" | Constraints
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.1#Ex3 3.1#Ex3] || [[Item:Q1070|<math>\ln_{0}(x) = x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ln_{0}(x) = x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">$0[0]ln()*(x) = x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[$0, 0]Log[]*(x) == x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.1#Ex4 3.1#Ex4] || [[Item:Q1071|<math>\ln_{\ell}(x) = \ln@{\ln_{\ell-1}(x)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln_{\ell}(x) = \ln@{\ln_{\ell-1}(x)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>$0[ell]ln()*(x) = [ell - 1]ln(ln()*(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[$0, \[ScriptL]]Log[]*(x) Subscript[== , \[ScriptL]- 1]Log[Log[]*(x)]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E1 3.2.E1] || [[Item:Q1076|<math>\mathbf{A}\mathbf{x} = \mathbf{b}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{A}\mathbf{x} = \mathbf{b}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*x = b</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*x == b</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E5 3.2.E5] || [[Item:Q1080|<math>\mathbf{A} = \mathbf{L}\mathbf{U}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{A} = \mathbf{L}\mathbf{U}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A = L*U</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A == L*U</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E11 3.2.E11] || [[Item:Q1087|<math>y_{j} = f_{j}-\ell_{j}y_{j-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y_{j} = f_{j}-\ell_{j}y_{j-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y[j] = f[j]- ell[j]*y[j - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[y, j] == Subscript[f, j]- Subscript[\[ScriptL], j]*Subscript[y, j - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E12 3.2.E12] || [[Item:Q1088|<math>x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j}</syntaxhighlight> || <math>j = n-1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[j] = (y[j]- u[j]*x[j + 1])/(b[j]- ell[j]*c[j - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, j] == (Subscript[y, j]- Subscript[u, j]*Subscript[x, j + 1])/(Subscript[b, j]- Subscript[\[ScriptL], j]*Subscript[c, j - 1])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.2#Ex3 3.2#Ex3] || [[Item:Q1089|<math>\|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[Norm[x], p] == ((Sum[(Abs[Subscript[x, j]])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]
Test Values: {Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.7142646344505674, 0.6191072997114272], Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]
Test Values: {Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E17 3.2.E17] || [[Item:Q1096|<math>\frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Error</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[Subscript[Norm[(x)^(*)- x], p],Subscript[Norm[x], p]] <= (Subscript[Norm[A], p]*Subscript[Norm[(A)^(- 1)], p])*Divide[Subscript[Norm[r], p],Subscript[Norm[b], p]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.2.E18 3.2.E18] || [[Item:Q1097|<math>\mathbf{A}\mathbf{x} = \lambda\mathbf{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{A}\mathbf{x} = \lambda\mathbf{x}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*x = lambda*x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*x == \[Lambda]*x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex3 3.3#Ex3] || [[Item:Q1113|<math>n_{0} = -\tfrac{1}{2}(n-\sigma)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>n_{0} = -\tfrac{1}{2}(n-\sigma)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n[0] = -(1)/(2)*(n - sigma)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[n, 0] == -Divide[1,2]*(n - \[Sigma])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex4 3.3#Ex4] || [[Item:Q1114|<math>n_{1} = \tfrac{1}{2}(n+\sigma)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>n_{1} = \tfrac{1}{2}(n+\sigma)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n[1] = (1)/(2)*(n + sigma)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[n, 1] == Divide[1,2]*(n + \[Sigma])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E9 3.3.E9] || [[Item:Q1115|<math>\sigma = \tfrac{1}{2}(1-(-1)^{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sigma = \tfrac{1}{2}(1-(-1)^{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sigma = (1)/(2)*(1 -(- 1)^(n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Sigma] == Divide[1,2]*(1 -(- 1)^(n))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E14 3.3.E14] || [[Item:Q1120|<math>f_{t} = (1-t)f_{0}+tf_{1}+R_{1,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = (1-t)f_{0}+tf_{1}+R_{1,t}</syntaxhighlight> || <math>0 < t, t < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = (1 - t)*f[0]+ t*f[1]+ R[1 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == (1 - t)*Subscript[f, 0]+ t*Subscript[f, 1]+ Subscript[R, 1 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E15 3.3.E15] || [[Item:Q1121|<math>c_{1} = \tfrac{1}{8}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{1} = \tfrac{1}{8}</syntaxhighlight> || <math>0 < t, t < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[1] = (1)/(8)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 1] == Divide[1,8]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E16 3.3.E16] || [[Item:Q1122|<math>f_{t} = \sum_{k=-1}^{1}A_{k}^{2}f_{k}+R_{2,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-1}^{1}A_{k}^{2}f_{k}+R_{2,t}</syntaxhighlight> || <math>\abs{t} < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(2)*f[k], k = - 1..1)+ R[2 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(2)*Subscript[f, k], {k, - 1, 1}, GenerateConditions->None]+ Subscript[R, 2 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex5 3.3#Ex5] || [[Item:Q1123|<math>A_{-1}^{2} = \tfrac{1}{2}t(t-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{2} = \tfrac{1}{2}t(t-1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(2) = (1)/(2)*t*(t - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(2) == Divide[1,2]*t*(t - 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex6 3.3#Ex6] || [[Item:Q1124|<math>A_{0}^{2} = 1-t^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{2} = 1-t^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(2) = 1 - (t)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(2) == 1 - (t)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex7 3.3#Ex7] || [[Item:Q1125|<math>A_{1}^{2} = \tfrac{1}{2}t(t+1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{2} = \tfrac{1}{2}t(t+1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(2) = (1)/(2)*t*(t + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(2) == Divide[1,2]*t*(t + 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E18 3.3.E18] || [[Item:Q1126|<math>c_{2} = 1/(9\sqrt{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{2} = 1/(9\sqrt{3})</syntaxhighlight> || <math>\abs{t} < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[2] = 1/(9*sqrt(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 2] == 1/(9*Sqrt[3])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E19 3.3.E19] || [[Item:Q1127|<math>f_{t} = \sum_{k=-1}^{2}A_{k}^{3}f_{k}+R_{3,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-1}^{2}A_{k}^{3}f_{k}+R_{3,t}</syntaxhighlight> || <math>-1 < t, t < 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(3)*f[k], k = - 1..2)+ R[3 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(3)*Subscript[f, k], {k, - 1, 2}, GenerateConditions->None]+ Subscript[R, 3 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex8 3.3#Ex8] || [[Item:Q1128|<math>A_{-1}^{3} = -\tfrac{1}{6}t(t-1)(t-2)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{3} = -\tfrac{1}{6}t(t-1)(t-2)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(3) = -(1)/(6)*t*(t - 1)*(t - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(3) == -Divide[1,6]*t*(t - 1)*(t - 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex9 3.3#Ex9] || [[Item:Q1129|<math>A_{0}^{3} = \tfrac{1}{2}(t^{2}-1)(t-2)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{3} = \tfrac{1}{2}(t^{2}-1)(t-2)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(3) = (1)/(2)*((t)^(2)- 1)*(t - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(3) == Divide[1,2]*((t)^(2)- 1)*(t - 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex10 3.3#Ex10] || [[Item:Q1130|<math>A_{1}^{3} = -\tfrac{1}{2}t(t+1)(t-2)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{3} = -\tfrac{1}{2}t(t+1)(t-2)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(3) = -(1)/(2)*t*(t + 1)*(t - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(3) == -Divide[1,2]*t*(t + 1)*(t - 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex11 3.3#Ex11] || [[Item:Q1131|<math>A_{2}^{3} = \tfrac{1}{6}t(t^{2}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}^{3} = \tfrac{1}{6}t(t^{2}-1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2])^(3) = (1)/(6)*t*((t)^(2)- 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2])^(3) == Divide[1,6]*t*((t)^(2)- 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E22 3.3.E22] || [[Item:Q1133|<math>f_{t} = \sum_{k=-2}^{2}A_{k}^{4}f_{k}+R_{4,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-2}^{2}A_{k}^{4}f_{k}+R_{4,t}</syntaxhighlight> || <math>\abs{t} < 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(4)*f[k], k = - 2..2)+ R[4 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(4)*Subscript[f, k], {k, - 2, 2}, GenerateConditions->None]+ Subscript[R, 4 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex12 3.3#Ex12] || [[Item:Q1134|<math>A_{-2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t-2)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t-2)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t - 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex13 3.3#Ex13] || [[Item:Q1135|<math>A_{-1}^{4} = -\tfrac{1}{6}t(t-1)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{4} = -\tfrac{1}{6}t(t-1)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(4) = -(1)/(6)*t*(t - 1)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(4) == -Divide[1,6]*t*(t - 1)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex14 3.3#Ex14] || [[Item:Q1136|<math>A_{0}^{4} = \tfrac{1}{4}(t^{2}-1)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{4} = \tfrac{1}{4}(t^{2}-1)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(4) = (1)/(4)*((t)^(2)- 1)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(4) == Divide[1,4]*((t)^(2)- 1)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex15 3.3#Ex15] || [[Item:Q1137|<math>A_{1}^{4} = -\tfrac{1}{6}t(t+1)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{4} = -\tfrac{1}{6}t(t+1)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(4) = -(1)/(6)*t*(t + 1)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(4) == -Divide[1,6]*t*(t + 1)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex16 3.3#Ex16] || [[Item:Q1138|<math>A_{2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t+2)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t+2)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t + 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t + 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E25 3.3.E25] || [[Item:Q1140|<math>f_{t} = \sum_{k=-2}^{3}A_{k}^{5}f_{k}+R_{5,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-2}^{3}A_{k}^{5}f_{k}+R_{5,t}</syntaxhighlight> || <math>-2 < t, t < 3</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(5)*f[k], k = - 2..3)+ R[5 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(5)*Subscript[f, k], {k, - 2, 3}, GenerateConditions->None]+ Subscript[R, 5 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex17 3.3#Ex17] || [[Item:Q1141|<math>A_{-2}^{5} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t-3)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-2}^{5} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t-3)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 2])^(5) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*(t - 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 2])^(5) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*(t - 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex18 3.3#Ex18] || [[Item:Q1142|<math>A_{-1}^{5} = \tfrac{1}{24}t(t-1)(t^{2}-4)(t-3)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{5} = \tfrac{1}{24}t(t-1)(t^{2}-4)(t-3)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(5) = (1)/(24)*t*(t - 1)*((t)^(2)- 4)*(t - 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(5) == Divide[1,24]*t*(t - 1)*((t)^(2)- 4)*(t - 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex19 3.3#Ex19] || [[Item:Q1143|<math>A_{0}^{5} = -\tfrac{1}{12}(t^{2}-1)(t^{2}-4)(t-3)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{5} = -\tfrac{1}{12}(t^{2}-1)(t^{2}-4)(t-3)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(5) = -(1)/(12)*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(5) == -Divide[1,12]*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex20 3.3#Ex20] || [[Item:Q1144|<math>A_{1}^{5} = \tfrac{1}{12}t(t+1)(t^{2}-4)(t-3)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{5} = \tfrac{1}{12}t(t+1)(t^{2}-4)(t-3)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(5) = (1)/(12)*t*(t + 1)*((t)^(2)- 4)*(t - 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(5) == Divide[1,12]*t*(t + 1)*((t)^(2)- 4)*(t - 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex21 3.3#Ex21] || [[Item:Q1145|<math>A_{2}^{5} = -\tfrac{1}{24}t(t^{2}-1)(t+2)(t-3)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}^{5} = -\tfrac{1}{24}t(t^{2}-1)(t+2)(t-3)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2])^(5) = -(1)/(24)*t*((t)^(2)- 1)*(t + 2)*(t - 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2])^(5) == -Divide[1,24]*t*((t)^(2)- 1)*(t + 2)*(t - 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex22 3.3#Ex22] || [[Item:Q1146|<math>A_{3}^{5} = \tfrac{1}{120}t(t^{2}-1)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{3}^{5} = \tfrac{1}{120}t(t^{2}-1)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[3])^(5) = (1)/(120)*t*((t)^(2)- 1)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 3])^(5) == Divide[1,120]*t*((t)^(2)- 1)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E28 3.3.E28] || [[Item:Q1148|<math>f_{t} = \sum_{k=-3}^{3}A_{k}^{6}f_{k}+R_{6,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-3}^{3}A_{k}^{6}f_{k}+R_{6,t}</syntaxhighlight> || <math>\abs{t} < 3</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(6)*f[k], k = - 3..3)+ R[6 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(6)*Subscript[f, k], {k, - 3, 3}, GenerateConditions->None]+ Subscript[R, 6 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex23 3.3#Ex23] || [[Item:Q1149|<math>A_{-3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t-3)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t-3)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex24 3.3#Ex24] || [[Item:Q1150|<math>A_{-2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex25 3.3#Ex25] || [[Item:Q1151|<math>A_{-1}^{6} = \tfrac{1}{48}t(t-1)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{6} = \tfrac{1}{48}t(t-1)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(6) = (1)/(48)*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(6) == Divide[1,48]*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex26 3.3#Ex26] || [[Item:Q1152|<math>A_{0}^{6} = -\tfrac{1}{36}(t^{2}-1)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{6} = -\tfrac{1}{36}(t^{2}-1)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(6) = -(1)/(36)*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(6) == -Divide[1,36]*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex27 3.3#Ex27] || [[Item:Q1153|<math>A_{1}^{6} = \tfrac{1}{48}t(t+1)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{6} = \tfrac{1}{48}t(t+1)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(6) = (1)/(48)*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(6) == Divide[1,48]*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex28 3.3#Ex28] || [[Item:Q1154|<math>A_{2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t+2)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t+2)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex29 3.3#Ex29] || [[Item:Q1155|<math>A_{3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t+3)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t+3)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E31 3.3.E31] || [[Item:Q1157|<math>f_{t} = \sum_{k=-3}^{4}A_{k}^{7}f_{k}+R_{7,t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{t} = \sum_{k=-3}^{4}A_{k}^{7}f_{k}+R_{7,t}</syntaxhighlight> || <math>-3 < t, t < 4</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[t] = sum((A[k])^(7)*f[k], k = - 3..4)+ R[7 , t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, t] == Sum[(Subscript[A, k])^(7)*Subscript[f, k], {k, - 3, 4}, GenerateConditions->None]+ Subscript[R, 7 , t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex30 3.3#Ex30] || [[Item:Q1158|<math>A_{-3}^{7} = -\tfrac{1}{5040}t(t^{2}-1)(t-3)(t-4)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-3}^{7} = -\tfrac{1}{5040}t(t^{2}-1)(t-3)(t-4)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 3])^(7) = -(1)/(5040)*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 3])^(7) == -Divide[1,5040]*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex31 3.3#Ex31] || [[Item:Q1159|<math>A_{-2}^{7} = \tfrac{1}{720}t(t^{2}-1)(t-2)(t-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-2}^{7} = \tfrac{1}{720}t(t^{2}-1)(t-2)(t-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 2])^(7) = (1)/(720)*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 2])^(7) == Divide[1,720]*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex32 3.3#Ex32] || [[Item:Q1160|<math>A_{-1}^{7} = -\tfrac{1}{240}t(t-1)(t-4)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1}^{7} = -\tfrac{1}{240}t(t-1)(t-4)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[- 1])^(7) = -(1)/(240)*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, - 1])^(7) == -Divide[1,240]*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex33 3.3#Ex33] || [[Item:Q1161|<math>A_{0}^{7} = \tfrac{1}{144}(t^{2}-1)(t-4)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0}^{7} = \tfrac{1}{144}(t^{2}-1)(t-4)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(7) = (1)/(144)*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(7) == Divide[1,144]*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex34 3.3#Ex34] || [[Item:Q1162|<math>A_{1}^{7} = -\tfrac{1}{144}t(t+1)(t-4)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}^{7} = -\tfrac{1}{144}t(t+1)(t-4)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[1])^(7) = -(1)/(144)*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 1])^(7) == -Divide[1,144]*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex35 3.3#Ex35] || [[Item:Q1163|<math>A_{2}^{7} = \tfrac{1}{240}t(t^{2}-1)(t+2)(t-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}^{7} = \tfrac{1}{240}t(t^{2}-1)(t+2)(t-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2])^(7) = (1)/(240)*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2])^(7) == Divide[1,240]*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex36 3.3#Ex36] || [[Item:Q1164|<math>A_{3}^{7} = -\tfrac{1}{720}t(t^{2}-1)(t+3)(t-4)(t^{2}-4)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{3}^{7} = -\tfrac{1}{720}t(t^{2}-1)(t+3)(t-4)(t^{2}-4)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[3])^(7) = -(1)/(720)*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 3])^(7) == -Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex37 3.3#Ex37] || [[Item:Q1165|<math>A_{4}^{7} = \tfrac{1}{5040}t(t^{2}-1)(t^{2}-4)(t^{2}-9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{4}^{7} = \tfrac{1}{5040}t(t^{2}-1)(t^{2}-4)(t^{2}-9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[4])^(7) = (1)/(5040)*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 4])^(7) == Divide[1,5040]*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex38 3.3#Ex38] || [[Item:Q1167|<math>f = f_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f = f_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f = f[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f == Subscript[f, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex39 3.3#Ex39] || [[Item:Q1168|<math>f = ({[z_{1}]}f-{[z_{0}]}f)/(z_{1}-z_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f = ({[z_{1}]}f-{[z_{0}]}f)/(z_{1}-z_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f = ((z[1])*f -(z[0])*f)/(z[1]- z[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f == ((Subscript[z, 1])*f -(Subscript[z, 0])*f)/(Subscript[z, 1]- Subscript[z, 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3#Ex40 3.3#Ex40] || [[Item:Q1169|<math>f = ({[z_{1},z_{2}]}f-{[z_{0},z_{1}]}f)/(z_{2}-z_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f = ({[z_{1},z_{2}]}f-{[z_{0},z_{1}]}f)/(z_{2}-z_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f = ([z[1], z[2]]*f -[z[0], z[1]]*f)/(z[2]- z[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f == ([Subscript[z, 1], Subscript[z, 2]]*f -[Subscript[z, 0], Subscript[z, 1]]*f)/(Subscript[z, 2]- Subscript[z, 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E39 3.3.E39] || [[Item:Q1174|<math>x(f) = [f_{0}]x+(f-f_{0})[f_{0},f_{1}]x+(f-f_{0})(f-f_{1})[f_{0},f_{1},f_{2}]x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x(f) = [f_{0}]x+(f-f_{0})[f_{0},f_{1}]x+(f-f_{0})(f-f_{1})[f_{0},f_{1},f_{2}]x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x(f) = (f[0])*x(+)*(f - f[0])*[f[0], f[1]]*x(+)*(f - f[0])*(f - f[1])*[f[0], f[1], f[2]]*x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[f] == (Subscript[f, 0])*x[+]*(f - Subscript[f, 0])*[Subscript[f, 0], Subscript[f, 1]]*x[+]*(f - Subscript[f, 0])*(f - Subscript[f, 1])*[Subscript[f, 0], Subscript[f, 1], Subscript[f, 2]]*x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.3.E40 3.3.E40] || [[Item:Q1175|<math>x = -2.2+1.44011\;1973(f-0.09614\;53780)+0.08865\;85832\*(f-0.09614\;53780)(f-0.02670\;63331)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = -2.2+1.44011\;1973(f-0.09614\;53780)+0.08865\;85832\*(f-0.09614\;53780)(f-0.02670\;63331)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex1 3.4#Ex1] || [[Item:Q1187|<math>B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(3) = -(1)/(6)*(2 - 6*t + 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(3) == -Divide[1,6]*(2 - 6*t + 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex2 3.4#Ex2] || [[Item:Q1188|<math>B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(3) = -(1)/(2)*(1 + 4*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(3) == -Divide[1,2]*(1 + 4*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex3 3.4#Ex3] || [[Item:Q1189|<math>B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(3) = (1)/(2)*(2 + 2*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(3) == Divide[1,2]*(2 + 2*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex4 3.4#Ex4] || [[Item:Q1190|<math>B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(3) = -(1)/(6)*(1 - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(3) == -Divide[1,6]*(1 - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex5 3.4#Ex5] || [[Item:Q1192|<math>B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(4) = (1)/(12)*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(4) == Divide[1,12]*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex6 3.4#Ex6] || [[Item:Q1193|<math>B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(4) = -(1)/(6)*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(4) == -Divide[1,6]*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex7 3.4#Ex7] || [[Item:Q1194|<math>B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(4) = -(1)/(2)*t*(5 - 2*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(4) == -Divide[1,2]*t*(5 - 2*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex8 3.4#Ex8] || [[Item:Q1195|<math>B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(4) = (1)/(6)*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(4) == Divide[1,6]*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex9 3.4#Ex9] || [[Item:Q1196|<math>B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(4) = -(1)/(12)*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(4) == -Divide[1,12]*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex10 3.4#Ex10] || [[Item:Q1198|<math>B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(5) = (1)/(120)*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(5) == Divide[1,120]*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex11 3.4#Ex11] || [[Item:Q1199|<math>B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(5) = -(1)/(24)*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(5) == -Divide[1,24]*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex12 3.4#Ex12] || [[Item:Q1200|<math>B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(5) = -(1)/(12)*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(5) == -Divide[1,12]*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex13 3.4#Ex13] || [[Item:Q1201|<math>B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(5) = (1)/(12)*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(5) == Divide[1,12]*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex14 3.4#Ex14] || [[Item:Q1202|<math>B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(5) = -(1)/(24)*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(5) == -Divide[1,24]*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex15 3.4#Ex15] || [[Item:Q1203|<math>B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(5) = (1)/(120)*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(5) == Divide[1,120]*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex16 3.4#Ex16] || [[Item:Q1205|<math>B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(6) = -(1)/(720)*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(6) == -Divide[1,720]*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex17 3.4#Ex17] || [[Item:Q1206|<math>B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(6) = (1)/(60)*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(6) == Divide[1,60]*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex18 3.4#Ex18] || [[Item:Q1207|<math>B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(6) = -(1)/(48)*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(6) == -Divide[1,48]*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex19 3.4#Ex19] || [[Item:Q1208|<math>B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(6) = -(1)/(18)*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(6) == -Divide[1,18]*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex20 3.4#Ex20] || [[Item:Q1209|<math>B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(6) = (1)/(48)*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(6) == Divide[1,48]*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex21 3.4#Ex21] || [[Item:Q1210|<math>B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(6) = -(1)/(60)*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(6) == -Divide[1,60]*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex22 3.4#Ex22] || [[Item:Q1211|<math>B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(6) = (1)/(720)*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(6) == Divide[1,720]*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex23 3.4#Ex23] || [[Item:Q1213|<math>B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(7) = -(1)/(5040)*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(7) == -Divide[1,5040]*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex24 3.4#Ex24] || [[Item:Q1214|<math>B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(7) = (1)/(720)*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(7) == Divide[1,720]*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex25 3.4#Ex25] || [[Item:Q1215|<math>B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(7) = -(1)/(240)*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(7) == -Divide[1,240]*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex26 3.4#Ex26] || [[Item:Q1216|<math>B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(7) = -(1)/(144)*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(7) == -Divide[1,144]*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex27 3.4#Ex27] || [[Item:Q1217|<math>B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(7) = (1)/(144)*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(7) == Divide[1,144]*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex28 3.4#Ex28] || [[Item:Q1218|<math>B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(7) = -(1)/(240)*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(7) == -Divide[1,240]*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex29 3.4#Ex29] || [[Item:Q1219|<math>B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(7) = (1)/(720)*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(7) == Divide[1,720]*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex30 3.4#Ex30] || [[Item:Q1220|<math>B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[4])^(7) = -(1)/(5040)*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 4])^(7) == -Divide[1,5040]*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.4.E19 3.4.E19] || [[Item:Q1223|<math>\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(factorial(k)) = (1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(k)!] == Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.
Test Values: {r = -1.5, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000000
Test Values: {r = -1.5, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1666666667
Test Values: {r = -1.5, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.
Test Values: {r = 1.5, k = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/3.5.E14 3.5.E14] || [[Item:Q1252|<math>\int_{0}^{\infty}e^{-pt}\BesselJ{0}@{t}\diff{t} = \frac{1}{\sqrt{p^{2}+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-pt}\BesselJ{0}@{t}\diff{t} = \frac{1}{\sqrt{p^{2}+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(exp(- p*t)*BesselJ(0, t), t = 0..infinity) = (1)/(sqrt((p)^(2)+ 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- p*t]*BesselJ[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[(p)^(2)+ 1]]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.732050807568877, -1.0]
Test Values: {Rule[p, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.4678898250138706, 0.39331989319032856]
Test Values: {Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5.E16 3.5.E16] || [[Item:Q1254|<math>w_{k} = \frac{g_{k}}{n}\left(1-\sum_{j=1}^{\floor{n/2}}\frac{b_{j}}{4j^{2}-1}\cos@{2jk\cpi/n}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{k} = \frac{g_{k}}{n}\left(1-\sum_{j=1}^{\floor{n/2}}\frac{b_{j}}{4j^{2}-1}\cos@{2jk\cpi/n}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[k] = (g[k])/(n)*(1 - sum((b[j])/(4*(j)^(2)- 1)*cos(2*j*k*Pi/n), j = 1..floor(n/2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, k] == Divide[Subscript[g, k],n]*(1 - Sum[Divide[Subscript[b, j],4*(j)^(2)- 1]*Cos[2*j*k*Pi/n], {j, 1, Floor[n/2]}, GenerateConditions->None])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [290 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3496793685+.1056624326*I
Test Values: {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5495724917+.2852208110*I
Test Values: {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5163460354+.3943375674*I
Test Values: {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5495724917+.2852208110*I
Test Values: {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5.E19 3.5.E19] || [[Item:Q1257|<math>E_{n}(f) = \gamma_{n}f^{(2n)}(\xi)/(2n)!</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>E_{n}(f) = \gamma_{n}f^{(2n)}(\xi)/(2n)!</syntaxhighlight> || <math>a < \xi, \xi < b</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(-(b - a)/(180)*(h)^(4)* (f(xi))^(4)) = (int((p[n])^(2)(x)* w(x), x = a..b))*(f(xi))^(2*n)/factorial(2*n)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(-Divide[b - a,180]*(h)^(4)* (f[\[Xi]])^(4)) == (Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None])*(f[\[Xi]])^(2*n)/(2*n)!</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex1 3.5#Ex1] || [[Item:Q1259|<math>[a,b] = [-1,1]</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>[a,b] = [-1,1]</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] = [- 1 , 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] == [- 1 , 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex2 3.5#Ex2] || [[Item:Q1260|<math>w(x) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex3 3.5#Ex3] || [[Item:Q1261|<math>\gamma_{n} = \frac{2^{2n+1}}{2n+1}\,\frac{(n!)^{4}}{((2n)!)^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{n} = \frac{2^{2n+1}}{2n+1}\,\frac{(n!)^{4}}{((2n)!)^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(int((p[n])^(2)(x)* w(x), x = a..b)) = ((2)^(2*n + 1))/(2*n + 1)*((factorial(n))^(4))/((factorial(2*n))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Divide[(2)^(2*n + 1),2*n + 1]*Divide[((n)!)^(4),((2*n)!)^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex4 3.5#Ex4] || [[Item:Q1262|<math>[a,b] = [-1,1]</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>[a,b] = [-1,1]</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] = [- 1 , 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] == [- 1 , 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex5 3.5#Ex5] || [[Item:Q1263|<math>w(x) = (1-x^{2})^{-1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = (1-x^{2})^{-1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = (1 - (x)^(2))^(- 1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == (1 - (x)^(2))^(- 1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5#Ex6 3.5#Ex6] || [[Item:Q1264|<math>\gamma_{n} = \frac{\cpi}{2^{2n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = \frac{\cpi}{2^{2n-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = (Pi)/((2)^(2*n - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Divide[Pi,(2)^(2*n - 1)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.570796327
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3926990818
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.9817477044e-1
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.570796327
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.5707963267948966
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.39269908169872414
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex7 3.5#Ex7] || [[Item:Q1265|<math>x_{k} = \cos@{\frac{2k-1}{2n}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{k} = \cos@{\frac{2k-1}{2n}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[k] = cos((2*k - 1)/(2*n)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, k] == Cos[Divide[2*k - 1,2*n]*Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254042+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1589186229+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2e-9+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254034+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.15891862259789125, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex8 3.5#Ex8] || [[Item:Q1266|<math>w_{k} = \frac{\cpi}{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{k} = \frac{\cpi}{n}</syntaxhighlight> || <math>k = 1</math> || <syntaxhighlight lang=mathematica>w[k] = (Pi)/(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, k] == Divide[Pi,n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.275567250+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7047709230+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1811721470+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.641592654+.8660254040*I
Test Values: {w[k] = -1/2+1/2*I*3^(1/2), k = 1, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.2755672498053543, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.7047709230104579, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex9 3.5#Ex9] || [[Item:Q1267|<math>x_{k} = \cos@{\frac{k}{n+1}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{k} = \cos@{\frac{k}{n+1}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[k] = cos((k)/(n + 1)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, k] == Cos[Divide[k,n + 1]*Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254042+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3660254038+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1589186229+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.866025404+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.3660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex10 3.5#Ex10] || [[Item:Q1268|<math>w_{k} = \frac{\cpi}{n+1}\sin^{2}@{\frac{k}{n+1}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{k} = \frac{\cpi}{n+1}\sin^{2}@{\frac{k}{n+1}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[k] = (Pi)/(n + 1)*(sin((k)/(n + 1)*Pi))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, k] == Divide[Pi,n + 1]*(Sin[Divide[k,n + 1]*Pi])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7047709230+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .806272408e-1+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4733263222+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.7047709230104579, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.08062724038699043, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex11 3.5#Ex11] || [[Item:Q1269|<math>\gamma_{n} = \frac{\cpi}{2^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = \frac{\cpi}{2^{2n+1}}</syntaxhighlight> || <math>\alpha = \beta, \beta = \tfrac{1}{2}</math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = (Pi)/((2)^(2*n + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Divide[Pi,(2)^(2*n + 1)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3926990818
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.9817477044e-1
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2454369261e-1
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3926990818
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.39269908169872414
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.09817477042468103
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex12 3.5#Ex12] || [[Item:Q1270|<math>x_{k} = +\cos@{\frac{2k}{2n+1}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{k} = +\cos@{\frac{2k}{2n+1}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[k] = + cos((2*k)/(2*n + 1)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, k] == + Cos[Divide[2*k,2*n + 1]*Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.366025404+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5570084102+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2425356024+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.366025403+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3660254037844388, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5570084094094913, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex12 3.5#Ex12] || [[Item:Q1270|<math>x_{k} = -\cos@{\frac{2k}{2n+1}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{k} = -\cos@{\frac{2k}{2n+1}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[k] = - cos((2*k)/(2*n + 1)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, k] == - Cos[Divide[2*k,2*n + 1]*Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3660254043+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.175042398+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.489515206+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3660254051+.5000000000*I
Test Values: {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [88 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.3660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1750423981593863, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex13 3.5#Ex13] || [[Item:Q1271|<math>w_{k} = \frac{4\cpi}{2n+1}\sin^{2}@{\frac{k}{2n+1}\cpi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{k} = \frac{4\cpi}{2n+1}\sin^{2}@{\frac{k}{2n+1}\cpi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[k] = (4*Pi)/(2*n + 1)*(sin((k)/(2*n + 1)*Pi))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, k] == Divide[4*Pi,2*n + 1]*(Sin[Divide[k,2*n + 1]*Pi])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.275567250+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.22894503e-2+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5280706399+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.275567248+.5000000000*I
Test Values: {w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.2755672498053543, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.0022894499063851326, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5#Ex14 3.5#Ex14] || [[Item:Q1272|<math>\gamma_{n} = \frac{\cpi}{2^{2n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = \frac{\cpi}{2^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = (Pi)/((2)^(2*n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Divide[Pi,(2)^(2*n)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7853981635
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1, alpha = 1/2, beta = -1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1963495409
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2, alpha = 1/2, beta = -1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4908738522e-1
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3, alpha = 1/2, beta = -1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7853981635
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1, alpha = 1/2, beta = -1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.7853981633974483
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, Rational[1, 2]], Rule[β, Rational[-1, 2]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.19634954084936207
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, Rational[1, 2]], Rule[β, Rational[-1, 2]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex15 3.5#Ex15] || [[Item:Q1273|<math>[a,b] = [-1,1]</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>[a,b] = [-1,1]</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] = [- 1 , 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] == [- 1 , 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex16 3.5#Ex16] || [[Item:Q1274|<math>w(x) = (1-x)^{\alpha}(1+x)^{\beta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = (1-x)^{\alpha}(1+x)^{\beta}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = (1 - x)^(alpha)*(1 + x)^(beta)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == (1 - x)^\[Alpha]*(1 + x)^\[Beta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5#Ex17 3.5#Ex17] || [[Item:Q1275|<math>\gamma_{n} = \dfrac{\EulerGamma@{n+\alpha+1}\EulerGamma@{n+\beta+1}\EulerGamma@{n+\alpha+\beta+1}}{(2n+\alpha+\beta+1)(\EulerGamma@{2n+\alpha+\beta+1})^{2}}2^{2n+\alpha+\beta+1}n!</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = \dfrac{\EulerGamma@{n+\alpha+1}\EulerGamma@{n+\beta+1}\EulerGamma@{n+\alpha+\beta+1}}{(2n+\alpha+\beta+1)(\EulerGamma@{2n+\alpha+\beta+1})^{2}}2^{2n+\alpha+\beta+1}n!</syntaxhighlight> || <math>\alpha > -1, \beta > -1, \realpart@@{(n+\alpha+1)} > 0, \realpart@@{(n+\beta+1)} > 0, \realpart@@{(n+\alpha+\beta+1)} > 0, \realpart@@{(2n+\alpha+\beta+1)} > 0</math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = (GAMMA(n + alpha + 1)*GAMMA(n + beta + 1)*GAMMA(n + alpha + beta + 1))/((2*n + alpha + beta + 1)*(GAMMA(2*n + alpha + beta + 1))^(2))*(2)^(2*n + alpha + beta + 1)* factorial(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Divide[Gamma[n + \[Alpha]+ 1]*Gamma[n + \[Beta]+ 1]*Gamma[n + \[Alpha]+ \[Beta]+ 1],(2*n + \[Alpha]+ \[Beta]+ 1)*(Gamma[2*n + \[Alpha]+ \[Beta]+ 1])^(2)]*(2)^(2*n + \[Alpha]+ \[Beta]+ 1)* (n)!</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1963495408
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4090615438e-1
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.9203884728e-2
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1963495408
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex19 3.5#Ex19] || [[Item:Q1277|<math>w(x) = x^{\alpha}e^{-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = x^{\alpha}e^{-x}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = (x)^(alpha)* exp(- x)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == (x)^\[Alpha]* Exp[- x]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5#Ex20 3.5#Ex20] || [[Item:Q1278|<math>\gamma_{n} = n!\,\EulerGamma@{n+\alpha+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = n!\,\EulerGamma@{n+\alpha+1}</syntaxhighlight> || <math>\alpha > -1, \realpart@@{(n+\alpha+1)} > 0</math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = factorial(n)*GAMMA(n + alpha + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == (n)!*Gamma[n + \[Alpha]+ 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.323350970
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -23.26345680
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -314.0566667
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.323350970
Test Values: {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.3233509704478426
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -23.2634567931349
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex21 3.5#Ex21] || [[Item:Q1279|<math>(a,b) = (-\infty,\infty)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a,b) = (-\infty,\infty)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a , b) = (- infinity , infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a , b) == (- Infinity , Infinity)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex22 3.5#Ex22] || [[Item:Q1280|<math>w(x) = e^{-x^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = e^{-x^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = exp(- (x)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == Exp[- (x)^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5#Ex23 3.5#Ex23] || [[Item:Q1281|<math>\gamma_{n} = \sqrt{\cpi}\,\frac{n!}{2^{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma_{n} = \sqrt{\cpi}\,\frac{n!}{2^{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(int((p[n])^(2)(x)* w(x), x = a..b)) = sqrt(Pi)*(factorial(n))/((2)^(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Integrate[(Subscript[p, n])^(2)[x]* w[x], {x, a, b}, GenerateConditions->None]) == Sqrt[Pi]*Divide[(n)!,(2)^(n)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.8862269255
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8862269255
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.329340388
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8862269255
Test Values: {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.8862269254527579
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.8862269254527579
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5#Ex24 3.5#Ex24] || [[Item:Q1282|<math>[a,b] = [0,1]</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>[a,b] = [0,1]</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] = [0 , 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">[a , b] == [0 , 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5#Ex25 3.5#Ex25] || [[Item:Q1283|<math>w(x) = \ln@{1/x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(x) = \ln@{1/x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(x) = ln(1/x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[x] == Log[1/x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.704503214+.7500000000*I
Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2601344786+.2500000000*I
Test Values: {w = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.425197989+1.*I
Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3445348919+1.299038106*I
Test Values: {w = -1/2+1/2*I*3^(1/2), x = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7045032137848224, 0.7499999999999999]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.26013447866772593, 0.24999999999999997]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5.E30 3.5.E30] || [[Item:Q1284|<math>p_{k+1}(x) = (x-\alpha_{k})p_{k}(x)-\beta_{k}p_{k-1}(x)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{k+1}(x) = (x-\alpha_{k})p_{k}(x)-\beta_{k}p_{k-1}(x)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[k + 1](x) = (x - alpha[k])*p[k](x)- beta[k]*p[k - 1](x)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, k + 1][x] == (x - Subscript[\[Alpha], k])*Subscript[p, k][x]- Subscript[\[Beta], k]*Subscript[p, k - 1][x]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.5.E32 3.5.E32] || [[Item:Q1286|<math>w_{k} = \beta_{0}v_{k,1}^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{k} = \beta_{0}v_{k,1}^{2}</syntaxhighlight> || <math>k = 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[k] = beta[0]*(v[k , 1])^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, k] == Subscript[\[Beta], 0]*(Subscript[v, k , 1])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.5.E37 3.5.E37] || [[Item:Q1292|<math>\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta}\zeta^{-s}p_{k}(1/\zeta)p_{\ell}(1/\zeta)\diff{\zeta} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta}\zeta^{-s}p_{k}(1/\zeta)p_{\ell}(1/\zeta)\diff{\zeta} = 0</syntaxhighlight> || <math>k \neq \ell</math> || <syntaxhighlight lang=mathematica>int(exp(zeta)*(zeta)^(- s)* p[k]*(1/zeta)*p[ell]*(1/zeta), zeta = c - I*infinity..c + I*infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[\[Zeta]]*\[Zeta]^(- s)* Subscript[p, k]*(1/\[Zeta])*Subscript[p, \[ScriptL]]*(1/\[Zeta]), {\[Zeta], c - I*Infinity, c + I*Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.0699801238394655, 1.7724538509055168]
Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[Subscript[p, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.0699801238394655, 1.7724538509055168]
Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[Subscript[p, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.5.E42 3.5.E42] || [[Item:Q1298|<math>\erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta-2\lambda\sqrt{\zeta}}\frac{\diff{\zeta}}{\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta-2\lambda\sqrt{\zeta}}\frac{\diff{\zeta}}{\zeta}</syntaxhighlight> || <math>c > 0</math> || <syntaxhighlight lang=mathematica>erfc(lambda) = (1)/(2*Pi*I)*int(exp(zeta - 2*lambda*sqrt(zeta))*(1)/(zeta), zeta = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[\[Lambda]] == Divide[1,2*Pi*I]*Integrate[Exp[\[Zeta]- 2*\[Lambda]*Sqrt[\[Zeta]]]*Divide[1,\[Zeta]], {\[Zeta], c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9788588170e-1-.2531649186*I
Test Values: {c = 1.5, lambda = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.977726380-.8570608782*I
Test Values: {c = 1.5, lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2227361984e-1+.8570608782*I
Test Values: {c = 1.5, lambda = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.902114118+.2531649186*I
Test Values: {c = 1.5, lambda = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/3.5.E44 3.5.E44] || [[Item:Q1300|<math>\erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\lambda^{2}(t-2\sqrt{t})}\frac{\diff{t}}{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\lambda^{2}(t-2\sqrt{t})}\frac{\diff{t}}{t}</syntaxhighlight> || <math>c > 0</math> || <syntaxhighlight lang=mathematica>erfc(lambda) = (1)/(2*Pi*I)*int(exp((lambda)^(2)*(t - 2*sqrt(t)))*(1)/(t), t = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[\[Lambda]] == Divide[1,2*Pi*I]*Integrate[Exp[\[Lambda]^(2)*(t - 2*Sqrt[t])]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9788588170e-1-.2531649186*I
Test Values: {c = 1.5, lambda = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.977726380-.8570608782*I
Test Values: {c = 1.5, lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2227361984e-1+.8570608782*I
Test Values: {c = 1.5, lambda = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.902114118+.2531649186*I
Test Values: {c = 1.5, lambda = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/3.5.E45 3.5.E45] || [[Item:Q1301|<math>\erfc@@{\lambda} = \frac{e^{-\lambda^{2}}}{2\cpi}\int_{-\cpi}^{\cpi}e^{-\lambda^{2}\tan^{2}@{\frac{1}{2}\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{\lambda} = \frac{e^{-\lambda^{2}}}{2\cpi}\int_{-\cpi}^{\cpi}e^{-\lambda^{2}\tan^{2}@{\frac{1}{2}\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(lambda) = (exp(- (lambda)^(2)))/(2*Pi)*int(exp(- (lambda)^(2)* (tan((1)/(2)*theta))^(2)), theta = - Pi..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[\[Lambda]] == Divide[Exp[- \[Lambda]^(2)],2*Pi]*Integrate[Exp[- \[Lambda]^(2)* (Tan[Divide[1,2]*\[Theta]])^(2)], {\[Theta], - Pi, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {lambda = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.804228236+.5063298371*I
Test Values: {lambda = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.932210292
Test Values: {lambda = -1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.9554527597185267, -1.7141217559576072]
Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.80422823640912, 0.5063298374329107]
Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.6.E3 3.6.E3] || [[Item:Q1307|<math>a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n]*w[n + 1]- b[n]*w[n]+ c[n]*w[n - 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n]+ Subscript[c, n]*Subscript[w, n - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.6.E5 3.6.E5] || [[Item:Q1309|<math>\sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(lambda[n]*w[n], n = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[\[Lambda], n]*Subscript[w, n], {n, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.6.E10 3.6.E10] || [[Item:Q1315|<math>p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[n + 1]*w[n] = p[n]*w[n + 1]+ exp(1)[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, n + 1]*Subscript[w, n] == Subscript[p, n]*Subscript[w, n + 1]+ Subscript[E, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.6.E11 3.6.E11] || [[Item:Q1316|<math>w_{n+1}-2nw_{n}+w_{n-1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{n+1}-2nw_{n}+w_{n-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[n + 1]- 2*n*w[n]+ w[n - 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.6.E14 3.6.E14] || [[Item:Q1319|<math>w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[n + 1]- 2*n*w[n]+ w[n - 1] = -(2/Pi)*(1 -(- 1)^(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == -(2/Pi)*(1 -(- 1)^(n))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.273239544+0.*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.732050808-1.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.190862072-2.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.927858596e-1+.3660254040*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.2732395447351628
Test Values: {Rule[n, 1], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.7320508075688774, -0.9999999999999999]
Test Values: {Rule[n, 2], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.6.E17 3.6.E17] || [[Item:Q1322|<math>a_{n}w_{n+1}-b_{n}w_{n} = d_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n}w_{n+1}-b_{n}w_{n} = d_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n]*w[n + 1]- b[n]*w[n] = d[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n] == Subscript[d, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex10 3.7#Ex10] || [[Item:Q1338|<math>A_{11}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{11}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[11](tau , z) = sum(((tau)^(s))/(factorial(s))*f[s](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 11][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[f, s][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex11 3.7#Ex11] || [[Item:Q1339|<math>A_{12}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{12}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[12](tau , z) = sum(((tau)^(s))/(factorial(s))*g[s](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 12][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[g, s][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex12 3.7#Ex12] || [[Item:Q1340|<math>A_{21}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s+1}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{21}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s+1}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[21](tau , z) = sum(((tau)^(s))/(factorial(s))*f[s + 1](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 21][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[f, s + 1][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex13 3.7#Ex13] || [[Item:Q1341|<math>A_{22}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s+1}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{22}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s+1}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[22](tau , z) = sum(((tau)^(s))/(factorial(s))*g[s + 1](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 22][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[g, s + 1][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex14 3.7#Ex14] || [[Item:Q1342|<math>b_{1}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1](tau , z) = sum(((tau)^(s))/(factorial(s))*h[s](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[h, s][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7#Ex15 3.7#Ex15] || [[Item:Q1343|<math>b_{2}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s+1}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{2}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s+1}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[2](tau , z) = sum(((tau)^(s))/(factorial(s))*h[s + 1](z), s = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 2][\[Tau], z] == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[h, s + 1][z], {s, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7.E13 3.7.E13] || [[Item:Q1347|<math>\mathbf{A}\mathbf{w} = \mathbf{b}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{A}\mathbf{w} = \mathbf{b}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*w = b</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A*w == b</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.7.E15 3.7.E15] || [[Item:Q1350|<math>\deriv[2]{w_{k}}{x}+(\lambda_{k}-q(x))w_{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w_{k}}{x}+(\lambda_{k}-q(x))w_{k} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w[k], [x$(2)])+(lambda[k]- q(x))*w[k] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[w, k], {x, 2}]+(Subscript[\[Lambda], k]- q[x])*Subscript[w, k] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2500000002-.4330127020*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2500000002-.4330127020*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2500000002-.4330127020*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4330127020-.2500000002*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = -1/2+1/2*I*3^(1/2), k = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.25000000000000006, -0.43301270189221924]
Test Values: {Rule[k, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.25000000000000006, -0.43301270189221924]
Test Values: {Rule[k, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.7.E16 3.7.E16] || [[Item:Q1351|<math>w_{k}(a) = w_{k}(b)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{k}(a) = w_{k}(b)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[k](a) = w[k](b)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, k][a] == Subscript[w, k][b]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8.E2 3.8.E2] || [[Item:Q1365|<math>z = \phi(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \phi(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = phi(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == \[Phi][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.8.E3 3.8.E3] || [[Item:Q1366|<math>\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(z[n + 1]- zeta) < A*(abs(z[n]- zeta))^(p)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Subscript[z, n + 1]- \[Zeta]] < A*(Abs[Subscript[z, n]- \[Zeta]])^(p)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. < 0.
Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < 0.
Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < 0.
Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.414213562 < 0.
Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex1 3.8#Ex1] || [[Item:Q1368|<math>x_{n+1} = \phi(x_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{n+1} = \phi(x_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[n + 1] = phi(x[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, n + 1] == \[Phi][Subscript[x, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.8#Ex2 3.8#Ex2] || [[Item:Q1369|<math>\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = x + x*(cot(x))^(2)- cot(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == x + x*(Cot[x])^(2)- Cot[x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.137590423+.7500000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .881577740e-1+.2500000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.144507621+1.*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.186628529+1.299038106*I
Test Values: {phi = -1/2+1/2*I*3^(1/2), x = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.1375904227343937, 0.7499999999999999]
Test Values: {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.186628528411051, 1.299038105676658]
Test Values: {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8.E6 3.8.E6] || [[Item:Q1370|<math>x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[2] = x[1]-(x[1]- x[0])/(f[1]- f[0])*f[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, 2] == Subscript[x, 1]-Divide[Subscript[x, 1]- Subscript[x, 0],Subscript[f, 1]- Subscript[f, 0]]*Subscript[f, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8.E7 3.8.E7] || [[Item:Q1371|<math>z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = z[n]-((phi(z[n])- z[n])^(2))/(phi(phi(z[n]))- 2*phi(z[n])+ z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == Subscript[z, n]-Divide[(\[Phi][Subscript[z, n]]- Subscript[z, n])^(2),\[Phi][\[Phi][Subscript[z, n]]]- 2*\[Phi][Subscript[z, n]]+ Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex3 3.8#Ex3] || [[Item:Q1373|<math>z_{n+1} = \phi(z_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex4 3.8#Ex4] || [[Item:Q1374|<math>\phi(z) = \frac{3z^{4}+1}{4z^{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi(z) = \frac{3z^{4}+1}{4z^{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi(z) = (3*(z)^(4)+ 1)/(4*(z)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Phi][z] == Divide[3*(z)^(4)+ 1,4*(z)^(3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex7 3.8#Ex7] || [[Item:Q1377|<math>\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*s = (r[3]*q[0]- r[2]*q[1])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*s == Divide[Subscript[r, 3]*Subscript[q, 0]- Subscript[r, 2]*Subscript[q, 1],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex8 3.8#Ex8] || [[Item:Q1378|<math>\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*t = (ell*q[1]- r[2]*q[0])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*t == Divide[\[ScriptL]*Subscript[q, 1]- Subscript[r, 2]*Subscript[q, 0],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8#Ex9 3.8#Ex9] || [[Item:Q1379|<math>\ell = sr_{2}+tr_{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell = sr_{2}+tr_{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell = s*r[2]+ t*r[3]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[ScriptL] == s*Subscript[r, 2]+ t*Subscript[r, 3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.8.E13 3.8.E13] || [[Item:Q1381|<math>\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(z, alpha) = -(diff(f, alpha))/(diff(f, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[z, \[Alpha]] == -Divide[D[f, \[Alpha]],D[f, z]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || [[Item:Q1384|<math>\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=a[19], diff( x, temp$(1) ) ) = -((20)^(19))/(factorial(19))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, {temp, 1}]/.temp-> Subscript[a, 19]) == -Divide[(20)^(19),(19)!]</syntaxhighlight> || Failure || Failure || Skip - No test values generated || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.309980412182177*^7
Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.309980412182177*^7
Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || [[Item:Q1384|<math>-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-((20)^(19))/(factorial(19)) = (- 4.30) * (10)^(7)</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[(20)^(19),(19)!] == (- 4.30) * (10)^(7)</syntaxhighlight> || Translation Error || Translation Error || Skip - symbolical successful subtest || Skip - symbolical successful subtest
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.8.E17 3.8.E17] || [[Item:Q1385|<math>z_{n+1} = \phi(z_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E1 3.9.E1] || [[Item:Q1386|<math>\lim_{n\to\infty}\frac{t_{n}-\sigma}{s_{n}-\sigma} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to\infty}\frac{t_{n}-\sigma}{s_{n}-\sigma} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((t[n]- sigma)/(s[n]- sigma), n = infinity) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[t, n]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E7 3.9.E7] || [[Item:Q1392|<math>t_{n} = s_{n}-\frac{(\Delta s_{n})^{2}}{\Delta^{2}s_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{n} = s_{n}-\frac{(\Delta s_{n})^{2}}{\Delta^{2}s_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[n] = s[n]-((Delta*s[n])^(2))/((Delta)^(2)* s[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, n] == Subscript[s, n]-Divide[(\[CapitalDelta]*Subscript[s, n])^(2),\[CapitalDelta]^(2)* Subscript[s, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E8 3.9.E8] || [[Item:Q1393|<math>\lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = \rho</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = \rho</syntaxhighlight> || <math>\abs{\rho} < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((s[n + 1]- sigma)/(s[n]- sigma), n = infinity) = rho</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[s, n + 1]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == \[Rho]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E9 3.9.E9] || [[Item:Q1394|<math>t_{n,2k} = \frac{H_{k+1}(s_{n})}{H_{k}(\Delta^{2}s_{n})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{n,2k} = \frac{H_{k+1}(s_{n})}{H_{k}(\Delta^{2}s_{n})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[n , 2*k] = (H[k + 1](s[n]))/(H[k]((Delta)^(2)* s[n]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, n , 2*k] == Divide[Subscript[H, k + 1][Subscript[s, n]],Subscript[H, k][\[CapitalDelta]^(2)* Subscript[s, n]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9#Ex1 3.9#Ex1] || [[Item:Q1396|<math>\varepsilon_{-1}^{(n)} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{-1}^{(n)} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(varepsilon[- 1])^(n) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[CurlyEpsilon], - 1])^(n) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9#Ex2 3.9#Ex2] || [[Item:Q1397|<math>\varepsilon_{0}^{(n)} = s_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{0}^{(n)} = s_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(varepsilon[0])^(n) = s[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[CurlyEpsilon], 0])^(n) == Subscript[s, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9#Ex3 3.9#Ex3] || [[Item:Q1398|<math>\varepsilon_{m+1}^{(n)} = \varepsilon_{m-1}^{(n+1)}+\frac{1}{\varepsilon_{m}^{(n+1)}-\varepsilon_{m}^{(n)}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{m+1}^{(n)} = \varepsilon_{m-1}^{(n+1)}+\frac{1}{\varepsilon_{m}^{(n+1)}-\varepsilon_{m}^{(n)}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(varepsilon[m + 1])^(n) = (varepsilon[m - 1])^(n + 1)+(1)/((varepsilon[m])^(n + 1)- (varepsilon[m])^(n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[CurlyEpsilon], m + 1])^(n) == (Subscript[\[CurlyEpsilon], m - 1])^(n + 1)+Divide[1,(Subscript[\[CurlyEpsilon], m])^(n + 1)- (Subscript[\[CurlyEpsilon], m])^(n)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E12 3.9.E12] || [[Item:Q1399|<math>s_{n} = \sum_{j=1}^{n}\frac{(-1)^{j+1}}{j^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>s_{n} = \sum_{j=1}^{n}\frac{(-1)^{j+1}}{j^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">s[n] = sum(((- 1)^(j + 1))/((j)^(2)), j = 1..n)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[s, n] == Sum[Divide[(- 1)^(j + 1),(j)^(2)], {j, 1, n}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.9.E13 3.9.E13] || [[Item:Q1400|<math>{\cal L}_{k}^{(n)}(s) = \frac{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}\ifrac{s_{n+j}}{a_{n+j+1}}}{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}/a_{n+j+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>{\cal L}_{k}^{(n)}(s) = \frac{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}\ifrac{s_{n+j}}{a_{n+j+1}}}{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}/a_{n+j+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(L[k])^(n)(s) = (sum((- 1)^(j)*binomial(k,j)*(((n + j + 1)^(k - 1))/((n + k + 1)^(k - 1)))*(s[n + j])/(a[n + j + 1]), j = 0..k))/(sum((- 1)^(j)*binomial(k,j)*(((n + j + 1)^(k - 1))/((n + k + 1)^(k - 1)))/a[n + j + 1], j = 0..k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[L, k])^(n)[s] == Divide[Sum[(- 1)^(j)*Binomial[k,j]*(Divide[(n + j + 1)^(k - 1),(n + k + 1)^(k - 1)])*Divide[Subscript[s, n + j],Subscript[a, n + j + 1]], {j, 0, k}, GenerateConditions->None],Sum[(- 1)^(j)*Binomial[k,j]*(Divide[(n + j + 1)^(k - 1),(n + k + 1)^(k - 1)])/Subscript[a, n + j + 1], {j, 0, k}, GenerateConditions->None]]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.9.E15 3.9.E15] || [[Item:Q1402|<math>\lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((s[n + 1]- sigma)/(s[n]- sigma), n = infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[s, n + 1]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.9.E16 3.9.E16] || [[Item:Q1403|<math>c_{j,k,n} = \frac{\Pochhammersym{\beta+n+j}{k-1}}{\Pochhammersym{\beta+n+k}{k-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{j,k,n} = \frac{\Pochhammersym{\beta+n+j}{k-1}}{\Pochhammersym{\beta+n+k}{k-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(((n + j + 1)^(k - 1))/((n + k + 1)^(k - 1))) = (pochhammer(beta + n + j, k - 1))/(pochhammer(beta + n + k, k - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[(n + j + 1)^(k - 1),(n + k + 1)^(k - 1)]) == Divide[Pochhammer[\[Beta]+ n + j, k - 1],Pochhammer[\[Beta]+ n + k, k - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 81]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.277777778e-1
Test Values: {beta = 1.5, j = 1, k = 2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.181818182e-1
Test Values: {beta = 1.5, j = 1, k = 2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.128205129e-1
Test Values: {beta = 1.5, j = 1, k = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.805594406e-1
Test Values: {beta = 1.5, j = 1, k = 3, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 81]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -0.02777777777777768
Test Values: {Rule[j, 1], Rule[k, 2], Rule[n, 1], Rule[β, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.018181818181818188
Test Values: {Rule[j, 1], Rule[k, 2], Rule[n, 2], Rule[β, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/3.9.E17 3.9.E17] || [[Item:Q1404|<math>c_{j,k,n} = \frac{\Pochhammersym{-\gamma-n-j}{k-1}}{\Pochhammersym{-\gamma-n-k}{k-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{j,k,n} = \frac{\Pochhammersym{-\gamma-n-j}{k-1}}{\Pochhammersym{-\gamma-n-k}{k-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(((n + j + 1)^(k - 1))/((n + k + 1)^(k - 1))) = (pochhammer(- gamma - n - j, k - 1))/(pochhammer(- gamma - n - k, k - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[(n + j + 1)^(k - 1),(n + k + 1)^(k - 1)]) == Divide[Pochhammer[- \[Gamma]- n - j, k - 1],Pochhammer[- \[Gamma]- n - k, k - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .295470259e-1
Test Values: {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .184734286e-1
Test Values: {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .126342713e-1
Test Values: {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1117465202
Test Values: {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 3, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.004408174927732822, -0.03290306559789975]
Test Values: {Rule[j, 1], Rule[k, 2], Rule[n, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.003359414702213348, -0.020895843920590226]
Test Values: {Rule[j, 1], Rule[k, 2], Rule[n, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex1 3.10#Ex1] || [[Item:Q1409|<math>b_{0} = u_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0} = u_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0] = u[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0] == Subscript[u, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex2 3.10#Ex2] || [[Item:Q1410|<math>b_{1} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex3 3.10#Ex3] || [[Item:Q1411|<math>a_{1} = u_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = u_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = u[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[u, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex4 3.10#Ex4] || [[Item:Q1412|<math>b_{n} = 1+\frac{u_{n}}{u_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = 1+\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = 1 +(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == 1 +Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex5 3.10#Ex5] || [[Item:Q1413|<math>a_{n} = -\frac{u_{n}}{u_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = -\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math>n \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = -(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == -Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex6 3.10#Ex6] || [[Item:Q1416|<math>e_{0}^{n} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{0}^{n} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[0])^(n) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, 0])^(n) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex7 3.10#Ex7] || [[Item:Q1417|<math>q_{1}^{n} = c_{n+1}/c_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{1}^{n} = c_{n+1}/c_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[1])^(n) = c[n + 1]/c[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, 1])^(n) == Subscript[c, n + 1]/Subscript[c, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex8 3.10#Ex8] || [[Item:Q1418|<math>e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[j])^(k) = (exp(1)[j - 1])^(k + 1)+ (q[j])^(k + 1)- (q[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, j])^(k) == (Subscript[E, j - 1])^(k + 1)+ (Subscript[q, j])^(k + 1)- (Subscript[q, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex9 3.10#Ex9] || [[Item:Q1419|<math>q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[j + 1])^(k) = (q[j])^(k + 1)*(exp(1)[j])^(k + 1)/(exp(1)[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, j + 1])^(k) == (Subscript[q, j])^(k + 1)*(Subscript[E, j])^(k + 1)/(Subscript[E, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex10 3.10#Ex10] || [[Item:Q1420|<math>a_{0} = c_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{0} = c_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[0] = c[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 0] == Subscript[c, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex11 3.10#Ex11] || [[Item:Q1421|<math>a_{1} = q_{1}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = q_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = (q[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == (Subscript[q, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex12 3.10#Ex12] || [[Item:Q1422|<math>a_{2} = e_{1}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{2} = e_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[2] = (exp(1)[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 2] == (Subscript[E, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex13 3.10#Ex13] || [[Item:Q1423|<math>a_{3} = q_{2}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{3} = q_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[3] = (q[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 3] == (Subscript[q, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex14 3.10#Ex14] || [[Item:Q1424|<math>a_{4} = e_{2}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{4} = e_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[4] = (exp(1)[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 4] == (Subscript[E, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex16 3.10#Ex16] || [[Item:Q1427|<math>u_{n} = b_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{n} = b_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[n] = b[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, n] == Subscript[b, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex17 3.10#Ex17] || [[Item:Q1428|<math>u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</syntaxhighlight> || <math>k = n-1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[k] = b[k]+(a[k + 1])/(u[k + 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, k] == Subscript[b, k]+Divide[Subscript[a, k + 1],Subscript[u, k + 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10.E14 3.10.E14] || [[Item:Q1430|<math>C = \sum_{k=0}^{\infty}t_{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C = \sum_{k=0}^{\infty}t_{k}</syntaxhighlight> || <math>a_{n} \neq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(b[0]+(a[1])/(b[1]+(a[2])/(b[2]+ ..))) = sum(t[k], k = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[b, 0]+Divide[Subscript[a, 1],Subscript[b, 1]+Divide[Subscript[a, 2],Subscript[b, 2]+ \[Ellipsis]]]) == Sum[Subscript[t, k], {k, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex18 3.10#Ex18] || [[Item:Q1431|<math>t_{0} = a_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{0} = a_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[0] = a[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, 0] == Subscript[a, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex19 3.10#Ex19] || [[Item:Q1432|<math>t_{k} = \rho_{k}t_{k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{k} = \rho_{k}t_{k-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[k] = rho[k]*t[k - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, k] == Subscript[\[Rho], k]*Subscript[t, k - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex20 3.10#Ex20] || [[Item:Q1433|<math>\rho_{0} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{0} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[0] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex21 3.10#Ex21] || [[Item:Q1434|<math>\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[k] = (a[k]*(1 + rho[k - 1]))/(1 - a[k]*(1 + rho[k - 1]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], k] == Divide[Subscript[a, k]*(1 + Subscript[\[Rho], k - 1]),1 - Subscript[a, k]*(1 + Subscript[\[Rho], k - 1])]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex22 3.10#Ex22] || [[Item:Q1435|<math>C_{0} = b_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{0} = b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[0] = b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 0] == Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex23 3.10#Ex23] || [[Item:Q1436|<math>D_{1} = 1/b_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{1} = 1/b_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[1] = 1/b[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, 1] == 1/Subscript[b, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.10#Ex26 3.10#Ex26] || [[Item:Q1439|<math>D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[n] = (1)/(D[n - 1]*a[n]+ b[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, n] == Divide[1,Subscript[D, n - 1]*Subscript[a, n]+ Subscript[b, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E5 3.11.E5] || [[Item:Q1446|<math>\sum_{k=0}^{n}x_{j}^{k}\delta a_{k} = (-1)^{j}(m_{j}-m)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{k=0}^{n}x_{j}^{k}\delta a_{k} = (-1)^{j}(m_{j}-m)</syntaxhighlight> || <math>j = 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((x[j])^(k)*delta*a[k], k = 0..n) = (- 1)^(j)*(((- 1)^(j)* epsilon[n](x[j]))- m)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[x, j])^(k)*\[Delta]*Subscript[a, k], {k, 0, n}, GenerateConditions->None] == (- 1)^(j)*(((- 1)^(j)* Subscript[\[Epsilon], n][Subscript[x, j]])- m)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.11.E6 3.11.E6] || [[Item:Q1447|<math>\ChebyshevpolyT{n}@{x} = \cos@{n\acos@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyT{n}@{x} = \cos@{n\acos@@{x}}</syntaxhighlight> || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>ChebyshevT(n, x) = cos(n*arccos(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevT[n, x] == Cos[n*ArcCos[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/3.11.E7 3.11.E7] || [[Item:Q1448|<math>\ChebyshevpolyT{n+1}@{x}-2x\ChebyshevpolyT{n}@{x}+\ChebyshevpolyT{n-1}@{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ChebyshevpolyT{n+1}@{x}-2x\ChebyshevpolyT{n}@{x}+\ChebyshevpolyT{n-1}@{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>ChebyshevT(n + 1, x)- 2*x*ChebyshevT(n, x)+ ChebyshevT(n - 1, x) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>ChebyshevT[n + 1, x]- 2*x*ChebyshevT[n, x]+ ChebyshevT[n - 1, x] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/3.11.E13 3.11.E13] || [[Item:Q1454|<math>\epsilon_{n}(x) = d_{n+1}\ChebyshevpolyT{n+1}@{\frac{2x-a-b}{b-a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\epsilon_{n}(x) = d_{n+1}\ChebyshevpolyT{n+1}@{\frac{2x-a-b}{b-a}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>epsilon[n](x) = d[n + 1]*ChebyshevT(n + 1, (2*x - a - b)/(b - a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Epsilon], n][x] == Subscript[d, n + 1]*ChebyshevT[n + 1, Divide[2*x - a - b,b - a]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(-infinity)-Float(infinity)*I
Test Values: {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(-infinity)-Float(infinity)*I
Test Values: {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(-infinity)-Float(infinity)*I
Test Values: {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(-infinity)-Float(infinity)*I
Test Values: {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 2, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[d, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[d, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E15 3.11.E15] || [[Item:Q1456|<math>u_{k} = 2xu_{k+1}-u_{k+2}+c_{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{k} = 2xu_{k+1}-u_{k+2}+c_{k}</syntaxhighlight> || <math>k = n-1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[k] = 2*x*u[k + 1]- u[k + 2]+ c[k]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, k] == 2*x*Subscript[u, k + 1]- Subscript[u, k + 2]+ Subscript[c, k]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E18 3.11.E18] || [[Item:Q1459|<math>m_{j} = (-1)^{j}\epsilon_{k,\ell}(x_{j})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m_{j} = (-1)^{j}\epsilon_{k,\ell}(x_{j})</syntaxhighlight> || <math>j = 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((- 1)^(j)* epsilon[n](x[j])) = (- 1)^(j)* epsilon[k , ell](x[j])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((- 1)^(j)* Subscript[\[Epsilon], n][Subscript[x, j]]) == (- 1)^(j)* Subscript[\[Epsilon], k , \[ScriptL]][Subscript[x, j]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E19 3.11.E19] || [[Item:Q1460|<math>R_{3,3}(x) = \frac{p_{0}+p_{1}x+p_{2}x^{2}+p_{3}x^{3}}{1+q_{1}x+q_{2}x^{2}+q_{3}x^{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>R_{3,3}(x) = \frac{p_{0}+p_{1}x+p_{2}x^{2}+p_{3}x^{3}}{1+q_{1}x+q_{2}x^{2}+q_{3}x^{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">R[3 , 3](x) = (p[0]+ p[1]*x + p[2]*(x)^(2)+ p[3]*(x)^(3))/(1 + q[1]*x + q[2]*(x)^(2)+ q[3]*(x)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[R, 3 , 3][x] == Divide[Subscript[p, 0]+ Subscript[p, 1]*x + Subscript[p, 2]*(x)^(2)+ Subscript[p, 3]*(x)^(3),1 + Subscript[q, 1]*x + Subscript[q, 2]*(x)^(2)+ Subscript[q, 3]*(x)^(3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11#E23X 3.11#E23X] || [[Item:Q1464|<math>\displaystyle a_{0} = c_{0}b_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle a_{0} = c_{0}b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[0] = c[0]*b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 0] == Subscript[c, 0]*Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11#E23Xa 3.11#E23Xa] || [[Item:Q1465|<math>\displaystyle a_{1} = c_{1}b_{0}+c_{0}b_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle a_{1} = c_{1}b_{0}+c_{0}b_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = c[1]*b[0]+ c[0]*b[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[c, 1]*Subscript[b, 0]+ Subscript[c, 0]*Subscript[b, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E25 3.11.E25] || [[Item:Q1472|<math>(N-C)^{-1}+(S-C)^{-1} = (W-C)^{-1}+(E-C)^{-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(N-C)^{-1}+(S-C)^{-1} = (W-C)^{-1}+(E-C)^{-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(N - C)^(- 1)+(S - C)^(- 1) = (W - C)^(- 1)+(E - C)^(- 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(N - C)^(- 1)+(S - C)^(- 1) == (W - C)^(- 1)+(E - C)^(- 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E34 3.11.E34] || [[Item:Q1482|<math>X_{k\ell} = \sum_{j=1}^{J}w(x_{j})\phi_{k}(x_{j})\phi_{\ell}(x_{j})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>X_{k\ell} = \sum_{j=1}^{J}w(x_{j})\phi_{k}(x_{j})\phi_{\ell}(x_{j})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">X[k*ell] = sum(w(x[j])* phi[k](x[j])* phi[ell](x[j]), j = 1..J)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[X, k*\[ScriptL]] == Sum[w[Subscript[x, j]]* Subscript[\[Phi], k][Subscript[x, j]]* Subscript[\[Phi], \[ScriptL]][Subscript[x, j]], {j, 1, J}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.11.E37 3.11.E37] || [[Item:Q1485|<math>\sum_{j=0}^{n-1}\phi_{k}(x_{j})\conj{\phi_{\ell}(x_{j})} = n\Kroneckerdelta{k}{\ell}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{j=0}^{n-1}\phi_{k}(x_{j})\conj{\phi_{\ell}(x_{j})} = n\Kroneckerdelta{k}{\ell}</syntaxhighlight> || <math>k = 0, \ell = 0</math> || <syntaxhighlight lang=mathematica>sum(phi[k](x[j])* conjugate(phi[ell](x[j])), j = 0..n - 1) = n*KroneckerDelta[k, ell]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Subscript[\[Phi], k][Subscript[x, j]]* Conjugate[Subscript[\[Phi], \[ScriptL]][Subscript[x, j]]], {j, 0, n - 1}, GenerateConditions->None] == n*KroneckerDelta[k, \[ScriptL]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[1.0, Times[-1.0, KroneckerDelta[1.0, ℓ]]]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[2.0, Times[-2.0, KroneckerDelta[1.0, ℓ]]]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E38 3.11.E38] || [[Item:Q1486|<math>f_{j} = \sum_{k=0}^{n-1}a_{k}\phi_{k}(x_{j})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{j} = \sum_{k=0}^{n-1}a_{k}\phi_{k}(x_{j})</syntaxhighlight> || <math>j = 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[j] = sum(a[k]*phi[k](x[j]), k = 0..n - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, j] == Sum[Subscript[a, k]*Subscript[\[Phi], k][Subscript[x, j]], {k, 0, n - 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.11.E39 3.11.E39] || [[Item:Q1487|<math>a_{k} = \frac{1}{n}\sum_{j=0}^{n-1}f_{j}\conj{\phi_{k}(x_{j})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{k} = \frac{1}{n}\sum_{j=0}^{n-1}f_{j}\conj{\phi_{k}(x_{j})}</syntaxhighlight> || <math>k = 0</math> || <syntaxhighlight lang=mathematica>a[k] = (1)/(n)*sum(f[j]*conjugate(phi[k](x[j])), j = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, k] == Divide[1,n]*Sum[Subscript[f, j]*Conjugate[Subscript[\[Phi], k][Subscript[x, j]]], {j, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 0.9999999999999999]
Test Values: {Rule[k, 1], Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 0.9999999999999999]
Test Values: {Rule[k, 1], Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11#Ex5 3.11#Ex5] || [[Item:Q1490|<math>f_{j} = \sum_{k=0}^{n-1}a_{k}\omega_{n}^{jk}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{j} = \sum_{k=0}^{n-1}a_{k}\omega_{n}^{jk}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[j] = sum(a[k]*(omega[n])^(j*k), k = 0..n - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, j] == Sum[Subscript[a, k]*(Subscript[\[Omega], n])^(j*k), {k, 0, n - 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.11#Ex6 3.11#Ex6] || [[Item:Q1491|<math>\omega_{n} = e^{2\cpi i/n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\omega_{n} = e^{2\cpi i/n}</syntaxhighlight> || <math>j = 0</math> || <syntaxhighlight lang=mathematica>omega[n] = exp(2*Pi*I/n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Omega], n] == Exp[2*Pi*I/n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [290 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1339745960+.4999999992*I
Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.866025404+.5000000004*I
Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.366025404-.3660254040*I
Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.500000000+.8660254032*I
Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [290 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.1339745962155613, 0.49999999999999994]
Test Values: {Rule[n, 1], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844388, 0.49999999999999994]
Test Values: {Rule[n, 2], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.11.E42 3.11.E42] || [[Item:Q1492|<math>\omega_{n}^{2(k-(n/2))} = \omega_{n/2}^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\omega_{n}^{2(k-(n/2))} = \omega_{n/2}^{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(omega[n])^(2*(k -(n/2))) = (omega[n/2])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Omega], n])^(2*(k -(n/2))) == (Subscript[\[Omega], n/2])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.12.E1 3.12.E1] || [[Item:Q1493|<math>\cpi = 3.14159\;26535\;89793\;23846\;\ldots</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cpi = 3.14159\;26535\;89793\;23846\;\ldots</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Pi = 3.14159265358979323846</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi == 3.14159265358979323846</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/3.12.E2 3.12.E2] || [[Item:Q1494|<math>\cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Pi = 4*int((1)/(1 + (t)^(2)), t = 0..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi == 4*Integrate[Divide[1,1 + (t)^(2)], {t, 0, 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.12.E3 3.12.E3] || [[Item:Q1495|<math>e = 2.71828\;18284\;59045\;23536\;\ldots</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e = 2.71828\;18284\;59045\;23536\;\ldots</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">exp(1) = 2.71828182845904523536</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">E == 2.71828182845904523536</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/3.12.E4 3.12.E4] || [[Item:Q1496|<math>\EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>gamma = 0.57721566490153286060</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerGamma == 0.57721566490153286060</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|}
</div>
</div>

Latest revision as of 16:30, 25 May 2021

Areas
3.1 Arithmetics and Error Measures
3.2 Linear Algebra
3.3 Interpolation
3.4 Differentiation
3.5 Quadrature
3.6 Linear Difference Equations
3.7 Ordinary Differential Equations
3.8 Nonlinear Equations
3.9 Acceleration of Convergence
3.10 Continued Fractions
3.11 Approximation Techniques
3.12 Mathematical Constants
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