Results of Exponential, Logarithmic, Sine, and Cosine Integrals: Difference between revisions

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Notation: 6.1 Special Notation
Properties: 6.2 Definitions and Interrelations
6.3 Graphics
6.4 Analytic Continuation
6.5 Further Interrelations
6.6 Power Series
6.7 Integral Representations
6.8 Inequalities
6.9 Continued Fraction
6.10 Other Series Expansions
6.11 Relations to Other Functions
6.12 Asymptotic Expansions
6.13 Zeros
6.14 Integrals
6.15 Sums
Applications: 6.16 Mathematical Applications
6.17 Physical Applications
Computation: 6.18 Methods of Computation
6.19 Tables
6.20 Approximations
6.21 Software

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-<div style="width: 100%; height: 75vh; overflow: auto;">
+<div style="-moz-column-count:2; column-count:2;">
-{| class="wikitable sortable" style="margin: 0;"
+; Notation : [[6.1|6.1 Special Notation]]<br>
-|-
+; Properties : [[6.2|6.2 Definitions and Interrelations]]<br>[[6.3|6.3 Graphics]]<br>[[6.4|6.4 Analytic Continuation]]<br>[[6.5|6.5 Further Interrelations]]<br>[[6.6|6.6 Power Series]]<br>[[6.7|6.7 Integral Representations]]<br>[[6.8|6.8 Inequalities]]<br>[[6.9|6.9 Continued Fraction]]<br>[[6.10|6.10 Other Series Expansions]]<br>[[6.11|6.11 Relations to Other Functions]]<br>[[6.12|6.12 Asymptotic Expansions]]<br>[[6.13|6.13 Zeros]]<br>[[6.14|6.14 Integrals]]<br>[[6.15|6.15 Sums]]<br>
-! scope="col" style="position: sticky; top: 0;" | DLMF
+; Applications : [[6.16|6.16 Mathematical Applications]]<br>[[6.17|6.17 Physical Applications]]<br>
-! scope="col" style="position: sticky; top: 0;" | Formula
+; Computation : [[6.18|6.18 Methods of Computation]]<br>[[6.19|6.19 Tables]]<br>[[6.20|6.20 Approximations]]<br>[[6.21|6.21 Software]]<br>
-! 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
-|-
-|-
-| [https://dlmf.nist.gov/6.2.E1 6.2.E1] || [[Item:Q2211|<math>\expintE@{z} = \int_{z}^{\infty}\frac{e^{-t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = \int_{z}^{\infty}\frac{e^{-t}}{t}\diff{t}</syntaxhighlight> || <math>z \neq 0</math> || <syntaxhighlight lang=mathematica>Ei(z) = int((exp(- t))/(t), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == Integrate[Divide[Exp[- t],t], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744989+3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E2 6.2.E2] || [[Item:Q2212|<math>\expintE@{z} = e^{-z}\int_{0}^{\infty}\frac{e^{-t}}{t+z}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = e^{-z}\int_{0}^{\infty}\frac{e^{-t}}{t+z}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \pi</math> || <syntaxhighlight lang=mathematica>Ei(z) = exp(- z)*int((exp(- t))/(t + z), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == Exp[- z]*Integrate[Divide[Exp[- t],t + z], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744989+3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E3 6.2.E3] || [[Item:Q2213|<math>\expintEin@{z} = \int_{0}^{z}\frac{1-e^{-t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEin@{z} = \int_{0}^{z}\frac{1-e^{-t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] + Ln[z] + EulerGamma == Integrate[Divide[1 - Exp[- t],t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -0.5235987755982988], Ln[Complex[0.8660254037844387, 0.49999999999999994]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -2.0943951023931953], Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.2.E4 6.2.E4] || [[Item:Q2214|<math>\expintE@{z} = \expintEin@{z}-\ln@@{z}-\EulerConstant</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = \expintEin@{z}-\ln@@{z}-\EulerConstant</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == ExpIntegralE[1, z] + Ln[z] + EulerGamma - Log[z]- EulerGamma</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.5235987755982988], Times[-1.0, Ln[Complex[0.8660254037844387, 0.49999999999999994]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 2.0943951023931953], Times[-1.0, Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.2.E6 6.2.E6] || [[Item:Q2216|<math>\expintEi@{-x} = -\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{-x} = -\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[- x] == - Integrate[Divide[Exp[- t],t], {t, x, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.2.E6 6.2.E6] || [[Item:Q2216|<math>-\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t} = -\expintE@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t} = -\expintE@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- int((exp(- t))/(t), t = x..infinity) = - Ei(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- Integrate[Divide[Exp[- t],t], {t, x, Infinity}, GenerateConditions->None] == - ExpIntegralE[1, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.201265867
-Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1055536899
-Test Values: {x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.2.E7 6.2.E7] || [[Item:Q2217|<math>\expintEi@{+ x} = -\expintEin@{- x}+\ln@@{x}+\EulerConstant</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{+ x} = -\expintEin@{- x}+\ln@@{x}+\EulerConstant</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[+ x] == - ExpIntegralE[1, - x] + Ln[- x] + EulerGamma + Log[x]+ EulerGamma</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.5598964379112301, -3.141592653589793], Times[-1.0, Ln[-1.5]]]
-Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.46128414924312044, -3.141592653589793], Times[-1.0, Ln[-0.5]]]
-Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.2.E7 6.2.E7] || [[Item:Q2217|<math>\expintEi@{- x} = -\expintEin@{+ x}+\ln@@{x}+\EulerConstant</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{- x} = -\expintEin@{+ x}+\ln@@{x}+\EulerConstant</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[- x] == - ExpIntegralE[1, + x] + Ln[+ x] + EulerGamma + Log[x]+ EulerGamma</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.5598964379112301, Times[-1.0, Ln[1.5]]]
-Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-0.46128414924312044, Times[-1.0, Ln[0.5]]]
-Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.2.E9 6.2.E9] || [[Item:Q2219|<math>\sinint@{z} = \int_{0}^{z}\frac{\sin@@{t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinint@{z} = \int_{0}^{z}\frac{\sin@@{t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Si(z) = int((sin(t))/(t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] == Integrate[Divide[Sin[t],t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E10 6.2.E10] || [[Item:Q2220|<math>\shiftsinint@{z} = -\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\shiftsinint@{z} = -\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ssi(z) = - int((sin(t))/(t), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] - Pi/2 == - Integrate[Divide[Sin[t],t], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E10 6.2.E10] || [[Item:Q2220|<math>-\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t} = \sinint@{z}-\tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t} = \sinint@{z}-\tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- int((sin(t))/(t), t = z..infinity) = Si(z)-(1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>- Integrate[Divide[Sin[t],t], {t, z, Infinity}, GenerateConditions->None] == SinIntegral[z]-Divide[1,2]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E11 6.2.E11] || [[Item:Q2221|<math>\cosint(z) = -\int_{z}^{\infty}\frac{\cos@@{t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosint(z) = -\int_{z}^{\infty}\frac{\cos@@{t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ci((z) ) = - int((cos(t))/(t), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CosIntegral[(z) ] == - Integrate[Divide[Cos[t],t], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || -
-|-
-| [https://dlmf.nist.gov/6.2#Ex1 6.2#Ex1] || [[Item:Q2224|<math>\lim_{x\to\infty}\sinint@{x} = \tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{x\to\infty}\sinint@{x} = \tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(Si(x), x = infinity) = (1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[SinIntegral[x], x -> Infinity, GenerateConditions->None] == Divide[1,2]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/6.2#Ex2 6.2#Ex2] || [[Item:Q2225|<math>\lim_{x\to\infty}\cosint@{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{x\to\infty}\cosint@{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit(Ci(x), x = infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[CosIntegral[x], x -> Infinity, GenerateConditions->None] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/6.2.E15 6.2.E15] || [[Item:Q2226|<math>\sinhint@{z} = \int_{0}^{z}\frac{\sinh@@{t}}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinhint@{z} = \int_{0}^{z}\frac{\sinh@@{t}}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Shi(z) = int((sinh(t))/(t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinhIntegral[z] == Integrate[Divide[Sinh[t],t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.2.E16 6.2.E16] || [[Item:Q2227|<math>\coshint@{z} = \EulerConstant+\ln@@{z}+\int_{0}^{z}\frac{\cosh@@{t}-1}{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\coshint@{z} = \EulerConstant+\ln@@{z}+\int_{0}^{z}\frac{\cosh@@{t}-1}{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Chi(z) = gamma + ln(z)+ int((cosh(t)- 1)/(t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CoshIntegral[z] == EulerGamma + Log[z]+ Integrate[Divide[Cosh[t]- 1,t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.4.E1 6.4.E1] || [[Item:Q2234|<math>\expintE@{z} = \expintEin@{z}-\Ln@@{z}-\EulerConstant</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = \expintEin@{z}-\Ln@@{z}-\EulerConstant</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == ExpIntegralE[1, z] + Ln[z] + EulerGamma - Log[z]- EulerGamma</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.5235987755982988], Times[-1.0, Ln[Complex[0.8660254037844387, 0.49999999999999994]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 2.0943951023931953], Times[-1.0, Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E2 6.4.E2] || [[Item:Q2235|<math>\expintE@{ze^{2m\pi i}} = \expintE@{z}-2m\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{ze^{2m\pi i}} = \expintE@{z}-2m\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(z*exp(2*m*Pi*I)) = Ei(z)- 2*m*Pi*I</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z*Exp[2*m*Pi*I]] == ExpIntegralE[1, z]- 2*m*Pi*I</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1e-8+6.283185310*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, m = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6e-8+12.56637063*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 2, m = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 18.84955592153876]
-Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 18.84955592153876]
-Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E3 6.4.E3] || [[Item:Q2236|<math>\expintE@{ze^{+\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant-\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{ze^{+\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant-\pi i</syntaxhighlight> || <math>|\phase@@{z}| \leq \pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z*Exp[+ Pi*I]] == ExpIntegralE[1, - z] + Ln[- z] + EulerGamma - Log[z]- EulerGamma - Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 3.6651914291880923], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 5.235987755982989], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E3 6.4.E3] || [[Item:Q2236|<math>\expintE@{ze^{-\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant+\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{ze^{-\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant+\pi i</syntaxhighlight> || <math>|\phase@@{z}| \leq \pi</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z*Exp[- Pi*I]] == ExpIntegralE[1, - z] + Ln[- z] + EulerGamma - Log[z]- EulerGamma + Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -2.6179938779914944], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -1.0471975511965976], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E4 6.4.E4] || [[Item:Q2237|<math>\cosint@{ze^{+\pi i}} = +\pi i+\cosint@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosint@{ze^{+\pi i}} = +\pi i+\cosint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ci(z*exp(+ Pi*I)) = + Pi*I + Ci(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CosIntegral[z*Exp[+ Pi*I]] == + Pi*I + CosIntegral[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185308*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-6.283185308*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E4 6.4.E4] || [[Item:Q2237|<math>\cosint@{ze^{-\pi i}} = -\pi i+\cosint@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosint@{ze^{-\pi i}} = -\pi i+\cosint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ci(z*exp(- Pi*I)) = - Pi*I + Ci(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CosIntegral[z*Exp[- Pi*I]] == - Pi*I + CosIntegral[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185308*I
-Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+6.283185308*I
-Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 6.283185307179585]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E5 6.4.E5] || [[Item:Q2238|<math>\coshint@{ze^{+\pi i}} = +\pi i+\coshint@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\coshint@{ze^{+\pi i}} = +\pi i+\coshint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Chi(z*exp(+ Pi*I)) = + Pi*I + Chi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CoshIntegral[z*Exp[+ Pi*I]] == + Pi*I + CoshIntegral[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185308*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.4.E5 6.4.E5] || [[Item:Q2238|<math>\coshint@{ze^{-\pi i}} = -\pi i+\coshint@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\coshint@{ze^{-\pi i}} = -\pi i+\coshint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Chi(z*exp(- Pi*I)) = - Pi*I + Chi(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CoshIntegral[z*Exp[- Pi*I]] == - Pi*I + CoshIntegral[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
-Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+6.283185308*I
-Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 6.283185307179586]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.5.E1 6.5.E1] || [[Item:Q2241|<math>\expintE@{-x+ i0} = -\expintEi@{x}- i\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{-x+ i0} = -\expintEi@{x}- i\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, - x + I*0] == - ExpIntegralEi[x]- I*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.5.E1 6.5.E1] || [[Item:Q2241|<math>\expintE@{-x- i0} = -\expintEi@{x}+ i\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{-x- i0} = -\expintEi@{x}+ i\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, - x - I*0] == - ExpIntegralEi[x]+ I*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
-Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.5.E2 6.5.E2] || [[Item:Q2242|<math>\expintEi@{x} = -\tfrac{1}{2}(\expintE@{-x+i0}+\expintE@{-x-i0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{x} = -\tfrac{1}{2}(\expintE@{-x+i0}+\expintE@{-x-i0})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[x] == -Divide[1,2]*(ExpIntegralE[1, - x + I*0]+ ExpIntegralE[1, - x - I*0])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -3.141592653589793]
-Test Values: {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -3.141592653589793]
-Test Values: {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.5.E3 6.5.E3] || [[Item:Q2243|<math>\tfrac{1}{2}(\expintEi@{x}+\expintE@{x}) = \sinhint@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2}(\expintEi@{x}+\expintE@{x}) = \sinhint@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(ExpIntegralEi[x]+ ExpIntegralE[1, x]) == SinhIntegral[x]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.5.E3 6.5.E3] || [[Item:Q2243|<math>\sinhint@{x} = -i\sinint@{ix}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinhint@{x} = -i\sinint@{ix}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Shi(x) = - I*Si(I*x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinhIntegral[x] == - I*SinIntegral[I*x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.5.E4 6.5.E4] || [[Item:Q2244|<math>\tfrac{1}{2}(\expintEi@{x}-\expintE@{x}) = \coshint@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2}(\expintEi@{x}-\expintE@{x}) = \coshint@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(ExpIntegralEi[x]- ExpIntegralE[1, x]) == CoshIntegral[x]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.5.E4 6.5.E4] || [[Item:Q2244|<math>\coshint@{x} = \cosint@{ix}-\tfrac{1}{2}\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\coshint@{x} = \cosint@{ix}-\tfrac{1}{2}\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Chi(x) = Ci(I*x)-(1)/(2)*Pi*I</syntaxhighlight> || <syntaxhighlight lang=mathematica>CoshIntegral[x] == CosIntegral[I*x]-Divide[1,2]*Pi*I</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.5.E5 6.5.E5] || [[Item:Q2245|<math>\sinint@{z} = \tfrac{1}{2}i(\expintE@{-iz}-\expintE@{iz})+\tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinint@{z} = \tfrac{1}{2}i(\expintE@{-iz}-\expintE@{iz})+\tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Si(z) = (1)/(2)*I*(Ei(- I*z)- Ei(I*z))+(1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] == Divide[1,2]*I*(ExpIntegralE[1, - I*z]- ExpIntegralE[1, I*z])+Divide[1,2]*Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592653+0.*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.141592654-.1e-9*I
-Test Values: {z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.141592653589793, 0.0]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.141592653589793, 0.0]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.5.E6 6.5.E6] || [[Item:Q2246|<math>\cosint@{z} = -\tfrac{1}{2}(\expintE@{iz}+\expintE@{-iz})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosint@{z} = -\tfrac{1}{2}(\expintE@{iz}+\expintE@{-iz})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ci(z) = -(1)/(2)*(Ei(I*z)+ Ei(- I*z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>CosIntegral[z] == -Divide[1,2]*(ExpIntegralE[1, I*z]+ ExpIntegralE[1, - I*z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8944744988+.632221722*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 3.141592653589793]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -3.141592653589793]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.6.E1 6.6.E1] || [[Item:Q2248|<math>\expintEi@{x} = \EulerConstant+\ln@@{x}+\sum_{n=1}^{\infty}\frac{x^{n}}{n!\thinspace n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{x} = \EulerConstant+\ln@@{x}+\sum_{n=1}^{\infty}\frac{x^{n}}{n!\thinspace n}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[x] == EulerGamma + Log[x]+ Sum[Divide[(x)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.6.E2 6.6.E2] || [[Item:Q2249|<math>\expintE@{z} = -\EulerConstant-\ln@@{z}-\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{n}}{n!\thinspace n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = -\EulerConstant-\ln@@{z}-\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{n}}{n!\thinspace n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(z) = - gamma - ln(z)- sum(((- 1)^(n)* (z)^(n))/(factorial(n)*n), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == - EulerGamma - Log[z]- Sum[Divide[(- 1)^(n)* (z)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744989+3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.6.E3 6.6.E3] || [[Item:Q2250|<math>\expintE@{z} = -\ln@@{z}+e^{-z}\sum_{n=0}^{\infty}\frac{z^{n}}{n!}\digamma@{n+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = -\ln@@{z}+e^{-z}\sum_{n=0}^{\infty}\frac{z^{n}}{n!}\digamma@{n+1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(z) = - ln(z)+ exp(- z)*sum(((z)^(n))/(factorial(n))*Psi(n + 1), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == - Log[z]+ Exp[- z]*Sum[Divide[(z)^(n),(n)!]*PolyGamma[n + 1], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247031*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744987+3.773814376*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.6.E4 6.6.E4] || [[Item:Q2251|<math>\expintEin@{z} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}z^{n}}{n!\thinspace n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEin@{z} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}z^{n}}{n!\thinspace n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] + Ln[z] + EulerGamma == Sum[Divide[(- 1)^(n - 1)* (z)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -0.5235987755982988], Ln[Complex[0.8660254037844387, 0.49999999999999994]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -2.0943951023931953], Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.6.E5 6.6.E5] || [[Item:Q2252|<math>\sinint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{(2n+1)!(2n+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{(2n+1)!(2n+1)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Si(z) = sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(2*n + 1)*(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] == Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(2*n + 1)!*(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.6.E6 6.6.E6] || [[Item:Q2253|<math>\cosint@{z} = \EulerConstant+\ln@@{z}+\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{2n}}{(2n)!(2n)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosint@{z} = \EulerConstant+\ln@@{z}+\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{2n}}{(2n)!(2n)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ci(z) = gamma + ln(z)+ sum(((- 1)^(n)* (z)^(2*n))/(factorial(2*n)*(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>CosIntegral[z] == EulerGamma + Log[z]+ Sum[Divide[(- 1)^(n)* (z)^(2*n),(2*n)!*(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.7.E1 6.7.E1] || [[Item:Q2254|<math>\int_{0}^{\infty}\frac{e^{-at}}{t+b}\diff{t} = \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\frac{e^{-at}}{t+b}\diff{t} = \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t}</syntaxhighlight> || <math>a > 0, b > 0</math> || <syntaxhighlight lang=mathematica>int((exp(- a*t))/(t + b), t = 0..infinity) = int((exp(I*a*t))/(t + I*b), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[- a*t],t + b], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Skip - symbolical successful subtest || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/6.7.E1 6.7.E1] || [[Item:Q2254|<math>\int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t} = e^{ab}\expintE@{ab}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t} = e^{ab}\expintE@{ab}</syntaxhighlight> || <math>a > 0, b > 0</math> || <syntaxhighlight lang=mathematica>int((exp(I*a*t))/(t + I*b), t = 0..infinity) = exp(a*b)*Ei(a*b)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}, GenerateConditions->None] == Exp[a*b]*ExpIntegralE[1, a*b]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -56.03273673
-Test Values: {a = 1.5, b = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.835422085
-Test Values: {a = 1.5, b = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/6.7.E2 6.7.E2] || [[Item:Q2255|<math>e^{x}\int_{0}^{\alpha}\frac{e^{-xt}}{1-t}\diff{t} = \expintEi@{x}-\expintEi@{(1-\alpha)x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{x}\int_{0}^{\alpha}\frac{e^{-xt}}{1-t}\diff{t} = \expintEi@{x}-\expintEi@{(1-\alpha)x}</syntaxhighlight> || <math>0 \leq \alpha, \alpha < 1, x > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[x]*Integrate[Divide[Exp[- x*t],1 - t], {t, 0, \[Alpha]}, GenerateConditions->None] == ExpIntegralEi[x]- ExpIntegralEi[(1 - \[Alpha])*x]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.7.E3 6.7.E3] || [[Item:Q2256|<math>\int_{x}^{\infty}\frac{e^{it}}{a^{2}+t^{2}}\diff{t} = \frac{i}{2a}\left(e^{a}\expintE@{a-ix}-e^{-a}\expintE@{-a-ix}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{x}^{\infty}\frac{e^{it}}{a^{2}+t^{2}}\diff{t} = \frac{i}{2a}\left(e^{a}\expintE@{a-ix}-e^{-a}\expintE@{-a-ix}\right)</syntaxhighlight> || <math>a > 0, x > 0</math> || <syntaxhighlight lang=mathematica>int((exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (I)/(2*a)*(exp(a)*Ei(a - I*x)- exp(- a)*Ei(- a - I*x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[I,2*a]*(Exp[a]*ExpIntegralE[1, a - I*x]- Exp[- a]*ExpIntegralE[1, - a - I*x])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -5.458727175-3.178550596*I
-Test Values: {a = 1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.924923680-4.406791455*I
-Test Values: {a = 1.5, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/6.7.E4 6.7.E4] || [[Item:Q2257|<math>\int_{x}^{\infty}\frac{te^{it}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{a}\expintE@{a-ix}+e^{-a}\expintE@{-a-ix}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{x}^{\infty}\frac{te^{it}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{a}\expintE@{a-ix}+e^{-a}\expintE@{-a-ix}\right)</syntaxhighlight> || <math>a > 0, x > 0</math> || <syntaxhighlight lang=mathematica>int((t*exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (1)/(2)*(exp(a)*Ei(a - I*x)+ exp(- a)*Ei(- a - I*x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[t*Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Exp[a]*ExpIntegralE[1, a - I*x]+ Exp[- a]*ExpIntegralE[1, - a - I*x])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -5.267453009+8.746914637*I
-Test Values: {a = 1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -7.302877906+3.948990541*I
-Test Values: {a = 1.5, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/6.7.E5 6.7.E5] || [[Item:Q2258|<math>\int_{x}^{\infty}\frac{e^{-t}}{a^{2}+t^{2}}\diff{t} = -\frac{1}{2ai}\left(e^{ia}\expintE@{x+ia}-e^{-ia}\expintE@{x-ia}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{x}^{\infty}\frac{e^{-t}}{a^{2}+t^{2}}\diff{t} = -\frac{1}{2ai}\left(e^{ia}\expintE@{x+ia}-e^{-ia}\expintE@{x-ia}\right)</syntaxhighlight> || <math>a > 0</math> || <syntaxhighlight lang=mathematica>int((exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity) = -(1)/(2*a*I)*(exp(I*a)*Ei(x + I*a)- exp(- I*a)*Ei(x - I*a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == -Divide[1,2*a*I]*(Exp[I*a]*ExpIntegralE[1, x + I*a]- Exp[- I*a]*ExpIntegralE[1, x - I*a])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.667239755-0.*I
-Test Values: {a = 1.5, x = 1.5, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7611670238-0.*I
-Test Values: {a = 1.5, x = .5, x = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/6.7.E6 6.7.E6] || [[Item:Q2259|<math>\int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{ia}\expintE@{x+ia}+e^{-ia}\expintE@{x-ia}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{ia}\expintE@{x+ia}+e^{-ia}\expintE@{x-ia}\right)</syntaxhighlight> || <math>a > 0</math> || <syntaxhighlight lang=mathematica>int((t*exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (1)/(2)*(exp(I*a)*Ei(x + I*a)+ exp(- I*a)*Ei(x - I*a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[t*Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Exp[I*a]*ExpIntegralE[1, x + I*a]+ Exp[- I*a]*ExpIntegralE[1, x - I*a])</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.610851888+0.*I
-Test Values: {a = 1.5, x = 1.5, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.934911868+0.*I
-Test Values: {a = 1.5, x = .5, x = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/6.7.E7 6.7.E7] || [[Item:Q2260|<math>\int_{0}^{1}\frac{e^{-at}\sin@{bt}}{t}\diff{t} = \imagpart@@{\expintEin@{a+ib}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}\frac{e^{-at}\sin@{bt}}{t}\diff{t} = \imagpart@@{\expintEin@{a+ib}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[- a*t]*Sin[b*t],t], {t, 0, 1}, GenerateConditions->None] == Im[ExpIntegralE[1, a + I*b] + Ln[a + I*b] + EulerGamma]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.7167380515760515, 5.551115123125783*^-17], Times[-1.0, Plus[-0.06866011182139653, Im[Ln[Complex[1.5, 1.5]]]]]]
-Test Values: {Rule[a, Rational[3, 2]], Rule[b, Rational[3, 2]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.7.E8 6.7.E8] || [[Item:Q2261|<math>\int_{0}^{1}\frac{e^{-at}(1-\cos@{bt})}{t}\diff{t} = \realpart@@{\expintEin@{a+ib}}-\expintEin@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}\frac{e^{-at}(1-\cos@{bt})}{t}\diff{t} = \realpart@@{\expintEin@{a+ib}}-\expintEin@{a}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Exp[- a*t]*(1 - Cos[b*t]),t], {t, 0, 1}, GenerateConditions->None] == Re[ExpIntegralE[1, a + I*b] + Ln[a + I*b] + EulerGamma]- ExpIntegralE[1, a] + Ln[a] + EulerGamma</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.8490131893081223, 0.0], Times[-1.0, Ln[1.5]], Times[-1.0, Plus[-0.04115544978502889, Re[Ln[Complex[1.5, 1.5]]]]]]
-Test Values: {Rule[a, Rational[3, 2]], Rule[b, Rational[3, 2]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.7.E9 6.7.E9] || [[Item:Q2262|<math>\shiftsinint@{z} = -\int_{0}^{\pi/2}e^{-z\cos@@{t}}\cos@{z\sin@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\shiftsinint@{z} = -\int_{0}^{\pi/2}e^{-z\cos@@{t}}\cos@{z\sin@@{t}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ssi(z) = - int(exp(- z*cos(t))*cos(z*sin(t)), t = 0..Pi/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] - Pi/2 == - Integrate[Exp[- z*Cos[t]]*Cos[z*Sin[t]], {t, 0, Pi/2}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592654+.1e-9*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.141592653+0.*I
-Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/6.7.E13 6.7.E13] || [[Item:Q2266|<math>\int_{0}^{\infty}\frac{\sin@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{e^{-zt}}{t^{2}+1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\frac{\sin@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{e^{-zt}}{t^{2}+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((sin(t))/(t + z), t = 0..infinity) = int((exp(- z*t))/((t)^(2)+ 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Sin[t],t + z], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.7.E14 6.7.E14] || [[Item:Q2267|<math>\int_{0}^{\infty}\frac{\cos@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{te^{-zt}}{t^{2}+1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\frac{\cos@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{te^{-zt}}{t^{2}+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((cos(t))/(t + z), t = 0..infinity) = int((t*exp(- z*t))/((t)^(2)+ 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[Cos[t],t + z], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[t*Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.8.E1 6.8.E1] || [[Item:Q2270|<math>\frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*ln(1 +(2)/(x)) < exp(x)*Ei(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*Log[1 +Divide[2,x]] < Exp[x]*ExpIntegralE[1, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8047189560 < .7488820189
-Test Values: {x = .5}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.8.E1 6.8.E1] || [[Item:Q2270|<math>e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(x)*Ei(x) < ln(1 +(1)/(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[x]*ExpIntegralE[1, x] < Log[1 +Divide[1,x]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 14.79533491 < .5108256240
-Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 36.60711558 < .4054651081
-Test Values: {x = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.8.E2 6.8.E2] || [[Item:Q2271|<math>\frac{x}{x+1} < xe^{x}\expintE@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{x}{x+1} < xe^{x}\expintE@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x)/(x + 1) < x*exp(x)*Ei(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[x,x + 1] < x*Exp[x]*ExpIntegralE[1, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.8.E2 6.8.E2] || [[Item:Q2271|<math>xe^{x}\expintE@{x} < \frac{x+1}{x+2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>xe^{x}\expintE@{x} < \frac{x+1}{x+2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x*exp(x)*Ei(x) < (x + 1)/(x + 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x*Exp[x]*ExpIntegralE[1, x] < Divide[x + 1,x + 2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 22.19300237 < .7142857143
-Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 73.21423116 < .7500000000
-Test Values: {x = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.8.E3 6.8.E3] || [[Item:Q2272|<math>\frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x*(x + 3))/((x)^(2)+ 4*x + 2) < x*exp(x)*Ei(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[x*(x + 3),(x)^(2)+ 4*x + 2] < x*Exp[x]*ExpIntegralE[1, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4117647059 < .3744410095
-Test Values: {x = .5}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.8.E3 6.8.E3] || [[Item:Q2272|<math>xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x*exp(x)*Ei(x) < ((x)^(2)+ 5*x + 2)/((x)^(2)+ 6*x + 6)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x*Exp[x]*ExpIntegralE[1, x] < Divide[(x)^(2)+ 5*x + 2,(x)^(2)+ 6*x + 6]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 22.19300237 < .6811594203
-Test Values: {x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 73.21423116 < .7272727273
-Test Values: {x = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10#Ex1 6.10#Ex1] || [[Item:Q2275|<math>c_{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10#Ex2 6.10#Ex2] || [[Item:Q2276|<math>c_{1} = -1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{1} = -1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[1] = - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 1] == - 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10#Ex3 6.10#Ex3] || [[Item:Q2277|<math>c_{2} = \tfrac{1}{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{2} = \tfrac{1}{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[2] = (1)/(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 2] == Divide[1,2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10#Ex4 6.10#Ex4] || [[Item:Q2278|<math>c_{3} = -\tfrac{1}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{3} = -\tfrac{1}{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[3] = -(1)/(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 3] == -Divide[1,3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10#Ex5 6.10#Ex5] || [[Item:Q2279|<math>c_{4} = \tfrac{1}{6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{4} = \tfrac{1}{6}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[4] = (1)/(6)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 4] == Divide[1,6]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.10.E3 6.10.E3] || [[Item:Q2280|<math>c_{k} = -\sum_{j=0}^{k-1}\frac{c_{j}}{k-j}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{k} = -\sum_{j=0}^{k-1}\frac{c_{j}}{k-j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[k] = - sum((c[j])/(k - j), j = 0..k - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, k] == - Sum[Divide[Subscript[c, j],k - j], {j, 0, k - 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/6.10.E4 6.10.E4] || [[Item:Q2281|<math>\sinint@{z} = z\sum_{n=0}^{\infty}\left(\sphBesselJ{n}@{\tfrac{1}{2}z}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinint@{z} = z\sum_{n=0}^{\infty}\left(\sphBesselJ{n}@{\tfrac{1}{2}z}\right)^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SinIntegral[z] == z*Sum[(SphericalBesselJ[n, Divide[1,2]*z])^(2), {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.10.E6 6.10.E6] || [[Item:Q2283|<math>\expintEi@{x} = \EulerConstant+\ln@@{\abs{x}}+\sum_{n=0}^{\infty}(-1)^{n}(x-a_{n})\left(\modsphBesseli{1}{n}@{\tfrac{1}{2}x}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEi@{x} = \EulerConstant+\ln@@{\abs{x}}+\sum_{n=0}^{\infty}(-1)^{n}(x-a_{n})\left(\modsphBesseli{1}{n}@{\tfrac{1}{2}x}\right)^{2}</syntaxhighlight> || <math>x \neq 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralEi[x] == EulerGamma + Log[Abs[x]]+ Sum[(- 1)^(n)*(x -((2*n + 1)*(1 -(- 1)^(n)+ PolyGamma[n + 1]- PolyGamma[1])))*(Sqrt[Divide[Pi, Divide[1,2]*x]/2] BesselI[(-1)^(1-1)*(n + 1/2), n])^(2), {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[2.318604676120101, Times[-1.0, NSum[Times[2.0943951023931953, Power[-1, n], Power[BesselI[Plus[Rational[1, 2], n], n], 2], Plus[1.5, Times[-1, Plus[1, Times[2, n]], Plus[1, Power[-1, Plus[1, n]], EulerGamma, PolyGamma[0, Plus[1, n]]]]]]
-Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[0.570151420521586, Times[-1.0, NSum[Times[6.283185307179586, Power[-1, n], Power[BesselI[Plus[Rational[1, 2], n], n], 2], Plus[0.5, Times[-1, Plus[1, Times[2, n]], Plus[1, Power[-1, Plus[1, n]], EulerGamma, PolyGamma[0, Plus[1, n]]]]]]
-Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.10.E8 6.10.E8] || [[Item:Q2285|<math>\expintEin@{z} = ze^{-z/2}\left(\modsphBesseli{1}{0}@{\tfrac{1}{2}z}+\sum_{n=1}^{\infty}\dfrac{2n+1}{n(n+1)}\modsphBesseli{1}{n}@{\tfrac{1}{2}z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintEin@{z} = ze^{-z/2}\left(\modsphBesseli{1}{0}@{\tfrac{1}{2}z}+\sum_{n=1}^{\infty}\dfrac{2n+1}{n(n+1)}\modsphBesseli{1}{n}@{\tfrac{1}{2}z}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] + Ln[z] + EulerGamma == z*Exp[- z/2]*(Sqrt[Divide[Pi, Divide[1,2]*z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0]+ Sum[Divide[2*n + 1,n*(n + 1)]*Sqrt[Divide[Pi, Divide[1,2]*z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], {n, 1, Infinity}, GenerateConditions->None])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.7449988338501623, -0.19274910655694033], Ln[Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-0.6244291912543926, -0.17523758490546462], NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[n, -1], Power[Plus[1, n], -1], Plus[1, Times[2, n]], Power[Pi, Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.31531322950964413, -1.02230061506208], Ln[Complex[-0.4999999999999998, 0.8660254037844387]], Times[Complex[0.11615580955286336, -1.278760766761026], NSum[Times[Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[n, -1], Power[Plus[1, n], -1], Plus[1, Times[2, n]], Power[Pi, Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.11.E1 6.11.E1] || [[Item:Q2286|<math>\expintE@{z} = \incGamma@{0}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = \incGamma@{0}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(z) = GAMMA(0, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == Gamma[0, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744989+3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/6.11.E2 6.11.E2] || [[Item:Q2287|<math>\expintE@{z} = e^{-z}\KummerconfhyperU@{1}{1}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expintE@{z} = e^{-z}\KummerconfhyperU@{1}{1}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(z) = exp(- z)*KummerU(1, 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[1, z] == Exp[- z]*HypergeometricU[1, 1, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.393548628+1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8944744991+3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.13.E1 6.13.E1] || [[Item:Q2297|<math>x_{0} = 0.37250\;74107\;81366\;63446\;19918\;66580\dots</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{0} = 0.37250\;74107\;81366\;63446\;19918\;66580\dots</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[0] = 0.372507410781366634461991866580</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, 0] == 0.372507410781366634461991866580</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/6.14.E1 6.14.E1] || [[Item:Q2299|<math>\int_{0}^{\infty}e^{-at}\expintE@{t}\diff{t} = \frac{1}{a}\ln@{1+a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\expintE@{t}\diff{t} = \frac{1}{a}\ln@{1+a}</syntaxhighlight> || <math>\realpart@@{a} > -1</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*Ei(t), t = 0..infinity) = (1)/(a)*ln(1 + a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*ExpIntegralE[1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*Log[1 + a]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 4]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1487623676-2.094395103*I
-Test Values: {a = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5753641448
-Test Values: {a = -.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 4]
-|-
-| [https://dlmf.nist.gov/6.14.E2 6.14.E2] || [[Item:Q2300|<math>\int_{0}^{\infty}e^{-at}\cosint@{t}\diff{t} = -\frac{1}{2a}\ln@{1+a^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\cosint@{t}\diff{t} = -\frac{1}{2a}\ln@{1+a^{2}}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*Ci(t), t = 0..infinity) = -(1)/(2*a)*ln(1 + (a)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*CosIntegral[t], {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,2*a]*Log[1 + (a)^(2)]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/6.14.E3 6.14.E3] || [[Item:Q2301|<math>\int_{0}^{\infty}e^{-at}\shiftsinint@{t}\diff{t} = -\frac{1}{a}\atan@@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\shiftsinint@{t}\diff{t} = -\frac{1}{a}\atan@@{a}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*Ssi(t), t = 0..infinity) = -(1)/(a)*arctan(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,a]*ArcTan[a]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -902994.0050351195
-Test Values: {Rule[a, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -902991.9106400171
-Test Values: {Rule[a, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.14.E4 6.14.E4] || [[Item:Q2302|<math>\int_{0}^{\infty}\expintE^{2}@{t}\diff{t} = 2\ln@@{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\expintE^{2}@{t}\diff{t} = 2\ln@@{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((Ei(t))^(2), t = 0..infinity) = 2*ln(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(ExpIntegralE[1, t])^(2), {t, 0, Infinity}, GenerateConditions->None] == 2*Log[2]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/6.14.E5 6.14.E5] || [[Item:Q2303|<math>\int_{0}^{\infty}\cos@@{t}\cosint@{t}\diff{t} = \int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\cos@@{t}\cosint@{t}\diff{t} = \int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(cos(t)*Ci(t), t = 0..infinity) = int(sin(t)*Ssi(t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Cos[t]*CosIntegral[t], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 902989.9925173485
-Test Values: {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.14.E5 6.14.E5] || [[Item:Q2303|<math>\int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t} = -\tfrac{1}{4}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t} = -\tfrac{1}{4}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(sin(t)*Ssi(t), t = 0..infinity) = -(1)/(4)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,4]*Pi</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -902989.9925173485
-Test Values: {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.14.E6 6.14.E6] || [[Item:Q2304|<math>\int_{0}^{\infty}\cosint^{2}@{t}\diff{t} = \int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\cosint^{2}@{t}\diff{t} = \int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((Ci(t))^(2), t = 0..infinity) = int((Ssi(t))^(2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(CosIntegral[t])^(2), {t, 0, Infinity}, GenerateConditions->None] == Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/6.14.E6 6.14.E6] || [[Item:Q2304|<math>\int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t} = \tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t} = \tfrac{1}{2}\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((Ssi(t))^(2), t = 0..infinity) = (1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/6.14.E7 6.14.E7] || [[Item:Q2305|<math>\int_{0}^{\infty}\cosint@{t}\shiftsinint@{t}\diff{t} = \ln@@{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\cosint@{t}\shiftsinint@{t}\diff{t} = \ln@@{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(Ci(t)*Ssi(t), t = 0..infinity) = ln(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[CosIntegral[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == Log[2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -902996.3337464853
-Test Values: {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.15.E1 6.15.E1] || [[Item:Q2306|<math>\sum_{n=1}^{\infty}\cosint@{\pi n} = \tfrac{1}{2}(\ln@@{2}-\EulerConstant)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}\cosint@{\pi n} = \tfrac{1}{2}(\ln@@{2}-\EulerConstant)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(Ci(Pi*n), n = 1..infinity) = (1)/(2)*(ln(2)- gamma)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[CosIntegral[Pi*n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[2]- EulerGamma)</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.05796575782920621, NSum[CosIntegral[Times[n, Pi]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.15.E2 6.15.E2] || [[Item:Q2307|<math>\sum_{n=1}^{\infty}\frac{\shiftsinint@{\pi n}}{n} = \tfrac{1}{2}\pi(\ln@@{\pi}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}\frac{\shiftsinint@{\pi n}}{n} = \tfrac{1}{2}\pi(\ln@@{\pi}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((Ssi(Pi*n))/(n), n = 1..infinity) = (1)/(2)*Pi*(ln(Pi)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[SinIntegral[Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*(Log[Pi]- 1)</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.22734117306968246, NSum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.15.E3 6.15.E3] || [[Item:Q2308|<math>\sum_{n=1}^{\infty}(-1)^{n}\cosint@{2\pi n} = 1-\ln@@{2}-\tfrac{1}{2}\EulerConstant</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}(-1)^{n}\cosint@{2\pi n} = 1-\ln@@{2}-\tfrac{1}{2}\EulerConstant</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(n)* Ci(2*Pi*n), n = 1..infinity) = 1 - ln(2)-(1)/(2)*gamma</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(n)* CosIntegral[2*Pi*n], {n, 1, Infinity}, GenerateConditions->None] == 1 - Log[2]-Divide[1,2]*EulerGamma</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.018244986989288337, NSum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.15.E4 6.15.E4] || [[Item:Q2309|<math>\sum_{n=1}^{\infty}(-1)^{n}\frac{\shiftsinint@{2\pi n}}{n} = \pi(\tfrac{3}{2}\ln@@{2}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}(-1)^{n}\frac{\shiftsinint@{2\pi n}}{n} = \pi(\tfrac{3}{2}\ln@@{2}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(n)*(Ssi(2*Pi*n))/(n), n = 1..infinity) = Pi*((3)/(2)*ln(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(n)*Divide[SinIntegral[2*Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Pi*(Divide[3,2]*Log[2]- 1)</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.12478648186560967, NSum[Times[Power[-1, n], Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[2, n, Pi]]]]
-Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/6.18#Ex1 6.18#Ex1] || [[Item:Q2315|<math>A_{n} = \int_{0}^{\infty}\frac{te^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} = \int_{0}^{\infty}\frac{te^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[n] = int((t*exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n] == Integrate[Divide[t*Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7485296696+.6226310704*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8043767351+.5871300239*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7485296693535908, 0.622631070403298]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8043767348683764, 0.5871300238783713]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.18#Ex2 6.18#Ex2] || [[Item:Q2316|<math>B_{n} = \int_{0}^{\infty}\frac{e^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>B_{n} = \int_{0}^{\infty}\frac{e^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>B[n] = int((exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[B, n] == Integrate[Divide[Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7390515864+.5822189558*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, B[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8115624973+.5498007781*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, B[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7390515861602941, 0.5822189558055343]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8115624970800986, 0.549800778092373]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/6.18#Ex3 6.18#Ex3] || [[Item:Q2317|<math>C_{n} = \int_{0}^{\infty}e^{-zt}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>C_{n} = \int_{0}^{\infty}e^{-zt}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>C[n] = int(exp(- z*t)*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[C, n] == Integrate[Exp[- z*t]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6165937696+.8168923194*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7435675872+.7346733636*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6165937693596737, 0.8168923194411848]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.7435675869838186, 0.7346733636356504]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 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/6.18#Ex4 6.18#Ex4] || [[Item:Q2318|<math>A_{n-1} = A_{n}+\frac{z}{2n}C_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{n-1} = A_{n}+\frac{z}{2n}C_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[n - 1] = A[n]+(z)/(2*n)*C[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, n - 1] == Subscript[A, n]+Divide[z,2*n]*Subscript[C, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.18#Ex5 6.18#Ex5] || [[Item:Q2319|<math>B_{n-1} = \frac{2nB_{n}+zA_{n-1}}{2n-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{n-1} = \frac{2nB_{n}+zA_{n-1}}{2n-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[n - 1] = (2*n*B[n]+ z*A[n - 1])/(2*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[2*n*Subscript[B, n]+ z*Subscript[A, n - 1],2*n - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/6.18#Ex6 6.18#Ex6] || [[Item:Q2320|<math>C_{n-1} = C_{n}+B_{n-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n-1} = C_{n}+B_{n-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n - 1] = C[n]+ B[n - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n - 1] == Subscript[C, n]+ Subscript[B, n - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|}
 </div>

Results of Exponential, Logarithmic, Sine, and Cosine Integrals: Difference between revisions

Latest revision as of 17:43, 25 May 2021

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