31.11: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11.E4 31.11.E4] || [[Item:Q9088|<math>L_{0}c_{0}+M_{0}c_{1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>L_{0}c_{0}+M_{0}c_{1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">L[0]*c[0]+ M[0]*c[1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[L, 0]*Subscript[c, 0]+ Subscript[M, 0]*Subscript[c, 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E4 31.11.E4] || <math qid="Q9088">L_{0}c_{0}+M_{0}c_{1} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>L_{0}c_{0}+M_{0}c_{1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">L[0]*c[0]+ M[0]*c[1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[L, 0]*Subscript[c, 0]+ Subscript[M, 0]*Subscript[c, 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11.E5 31.11.E5] || [[Item:Q9089|<math>K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">K[j]*c[j - 1]+ L[j]*c[j]+ M[j]*c[j + 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[K, j]*Subscript[c, j - 1]+ Subscript[L, j]*Subscript[c, j]+ Subscript[M, j]*Subscript[c, j + 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E5 31.11.E5] || <math qid="Q9089">K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">K[j]*c[j - 1]+ L[j]*c[j]+ M[j]*c[j + 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[K, j]*Subscript[c, j - 1]+ Subscript[L, j]*Subscript[c, j]+ Subscript[M, j]*Subscript[c, j + 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11.E6 31.11.E6] || [[Item:Q9090|<math>K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">K[j] = -((j + alpha - mu - 1)*(j + beta - mu - 1)*(j + gamma - mu - 1)*(j + lambda - 1))/((2*j + lambda - mu - 1)*(2*j + lambda - mu - 2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[K, j] == -Divide[(j + \[Alpha]- \[Mu]- 1)*(j + \[Beta]- \[Mu]- 1)*(j + \[Gamma]- \[Mu]- 1)*(j + \[Lambda]- 1),(2*j + \[Lambda]- \[Mu]- 1)*(2*j + \[Lambda]- \[Mu]- 2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E6 31.11.E6] || <math qid="Q9090">K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">K[j] = -((j + alpha - mu - 1)*(j + beta - mu - 1)*(j + gamma - mu - 1)*(j + lambda - 1))/((2*j + lambda - mu - 1)*(2*j + lambda - mu - 2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[K, j] == -Divide[(j + \[Alpha]- \[Mu]- 1)*(j + \[Beta]- \[Mu]- 1)*(j + \[Gamma]- \[Mu]- 1)*(j + \[Lambda]- 1),(2*j + \[Lambda]- \[Mu]- 1)*(2*j + \[Lambda]- \[Mu]- 2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/31.11.E7 31.11.E7] || [[Item:Q9091|<math>L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">L[j] = a*(lambda + j)*(mu - j)- q +((j + alpha - mu)*(j + beta - mu)*(j + gamma - mu)*(j + lambda))/((2*j + lambda - mu)*(2*j + lambda - mu + 1))+((j - alpha + lambda)*(j - beta + lambda)*(j - gamma + lambda)*(j - mu))/((2*j + lambda - mu)*(2*j + lambda - mu - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[L, j] == a*(\[Lambda]+ j)*(\[Mu]- j)- q +Divide[(j + \[Alpha]- \[Mu])*(j + \[Beta]- \[Mu])*(j + \[Gamma]- \[Mu])*(j + \[Lambda]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]+ 1)]+Divide[(j - \[Alpha]+ \[Lambda])*(j - \[Beta]+ \[Lambda])*(j - \[Gamma]+ \[Lambda])*(j - \[Mu]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]- 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E7 31.11.E7] || <math qid="Q9091">L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">L[j] = a*(lambda + j)*(mu - j)- q +((j + alpha - mu)*(j + beta - mu)*(j + gamma - mu)*(j + lambda))/((2*j + lambda - mu)*(2*j + lambda - mu + 1))+((j - alpha + lambda)*(j - beta + lambda)*(j - gamma + lambda)*(j - mu))/((2*j + lambda - mu)*(2*j + lambda - mu - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[L, j] == a*(\[Lambda]+ j)*(\[Mu]- j)- q +Divide[(j + \[Alpha]- \[Mu])*(j + \[Beta]- \[Mu])*(j + \[Gamma]- \[Mu])*(j + \[Lambda]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]+ 1)]+Divide[(j - \[Alpha]+ \[Lambda])*(j - \[Beta]+ \[Lambda])*(j - \[Gamma]+ \[Lambda])*(j - \[Mu]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]- 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11.E8 31.11.E8] || [[Item:Q9092|<math>M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[j] = -((j - alpha + lambda + 1)*(j - beta + lambda + 1)*(j - gamma + lambda + 1)*(j - mu + 1))/((2*j + lambda - mu + 1)*(2*j + lambda - mu + 2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[M, j] == -Divide[(j - \[Alpha]+ \[Lambda]+ 1)*(j - \[Beta]+ \[Lambda]+ 1)*(j - \[Gamma]+ \[Lambda]+ 1)*(j - \[Mu]+ 1),(2*j + \[Lambda]- \[Mu]+ 1)*(2*j + \[Lambda]- \[Mu]+ 2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E8 31.11.E8] || <math qid="Q9092">M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[j] = -((j - alpha + lambda + 1)*(j - beta + lambda + 1)*(j - gamma + lambda + 1)*(j - mu + 1))/((2*j + lambda - mu + 1)*(2*j + lambda - mu + 2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[M, j] == -Divide[(j - \[Alpha]+ \[Lambda]+ 1)*(j - \[Beta]+ \[Lambda]+ 1)*(j - \[Gamma]+ \[Lambda]+ 1)*(j - \[Mu]+ 1),(2*j + \[Lambda]- \[Mu]+ 1)*(2*j + \[Lambda]- \[Mu]+ 2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/31.11.E9 31.11.E9] || [[Item:Q9093|<math>M_{-1}P_{-1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M_{-1}P_{-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[- 1]*P[- 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[M, - 1]*Subscript[P, - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11.E9 31.11.E9] || <math qid="Q9093">M_{-1}P_{-1} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M_{-1}P_{-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[- 1]*P[- 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[M, - 1]*Subscript[P, - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/31.11#Ex1 31.11#Ex1] || [[Item:Q9094|<math>\lambda = \alpha</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \alpha</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = alpha</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Alpha]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex1 31.11#Ex1] || <math qid="Q9094">\lambda = \alpha</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \alpha</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = alpha</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Alpha]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/31.11#Ex2 31.11#Ex2] || [[Item:Q9095|<math>\mu = \beta-\epsilon</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \beta-\epsilon</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = beta - epsilon</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Beta]- \[Epsilon]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex2 31.11#Ex2] || <math qid="Q9095">\mu = \beta-\epsilon</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \beta-\epsilon</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = beta - epsilon</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Beta]- \[Epsilon]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11#Ex3 31.11#Ex3] || [[Item:Q9096|<math>\lambda = \beta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \beta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = beta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Beta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex3 31.11#Ex3] || <math qid="Q9096">\lambda = \beta</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \beta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = beta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Beta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11#Ex4 31.11#Ex4] || [[Item:Q9097|<math>\mu = \alpha-\epsilon</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \alpha-\epsilon</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = alpha - epsilon</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Alpha]- \[Epsilon]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex4 31.11#Ex4] || <math qid="Q9097">\mu = \alpha-\epsilon</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \alpha-\epsilon</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = alpha - epsilon</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Alpha]- \[Epsilon]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11#Ex5 31.11#Ex5] || [[Item:Q9100|<math>\lambda = \gamma+\delta-1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \gamma+\delta-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = gamma + delta - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Gamma]+ \[Delta]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex5 31.11#Ex5] || <math qid="Q9100">\lambda = \gamma+\delta-1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \gamma+\delta-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = gamma + delta - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Gamma]+ \[Delta]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/31.11#Ex6 31.11#Ex6] || [[Item:Q9101|<math>\mu = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex6 31.11#Ex6] || <math qid="Q9101">\mu = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/31.11#Ex7 31.11#Ex7] || [[Item:Q9102|<math>\lambda = \gamma</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \gamma</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = gamma</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Gamma]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex7 31.11#Ex7] || <math qid="Q9102">\lambda = \gamma</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \gamma</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = gamma</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Gamma]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11#Ex8 31.11#Ex8] || [[Item:Q9103|<math>\mu = \delta-1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \delta-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = delta - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Delta]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex8 31.11#Ex8] || <math qid="Q9103">\mu = \delta-1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \delta-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = delta - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Delta]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11#Ex9 31.11#Ex9] || [[Item:Q9104|<math>\lambda = \delta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \delta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = delta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Delta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex9 31.11#Ex9] || <math qid="Q9104">\lambda = \delta</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = \delta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = delta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == \[Delta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11#Ex10 31.11#Ex10] || [[Item:Q9105|<math>\mu = \gamma-1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \gamma-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = gamma - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Gamma]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex10 31.11#Ex10] || <math qid="Q9105">\mu = \gamma-1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \gamma-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = gamma - 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Gamma]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11#Ex11 31.11#Ex11] || [[Item:Q9106|<math>\lambda = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex11 31.11#Ex11] || <math qid="Q9106">\lambda = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/31.11#Ex12 31.11#Ex12] || [[Item:Q9107|<math>\mu = \gamma+\delta-2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \gamma+\delta-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = gamma + delta - 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Gamma]+ \[Delta]- 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/31.11#Ex12 31.11#Ex12] || <math qid="Q9107">\mu = \gamma+\delta-2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu = \gamma+\delta-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu = gamma + delta - 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Mu] == \[Gamma]+ \[Delta]- 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
|}
</div>
</div>

Latest revision as of 12:11, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
31.11.E4 L 0 ⁢ c 0 + M 0 ⁢ c 1 = 0 subscript 𝐿 0 subscript 𝑐 0 subscript 𝑀 0 subscript 𝑐 1 0 {\displaystyle{\displaystyle L_{0}c_{0}+M_{0}c_{1}=0}}
L_{0}c_{0}+M_{0}c_{1} = 0		 

L[0]*c[0]+ M[0]*c[1] = 0
 
Subscript[L, 0]*Subscript[c, 0]+ Subscript[M, 0]*Subscript[c, 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E5 K j ⁢ c j - 1 + L j ⁢ c j + M j ⁢ c j + 1 = 0 subscript 𝐾 𝑗 subscript 𝑐 𝑗 1 subscript 𝐿 𝑗 subscript 𝑐 𝑗 subscript 𝑀 𝑗 subscript 𝑐 𝑗 1 0 {\displaystyle{\displaystyle K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1}=0}}
K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0		 

K[j]*c[j - 1]+ L[j]*c[j]+ M[j]*c[j + 1] = 0
 
Subscript[K, j]*Subscript[c, j - 1]+ Subscript[L, j]*Subscript[c, j]+ Subscript[M, j]*Subscript[c, j + 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E6 K j = - ( j + α - μ - 1 ) ⁢ ( j + β - μ - 1 ) ⁢ ( j + γ - μ - 1 ) ⁢ ( j + λ - 1 ) ( 2 ⁢ j + λ - μ - 1 ) ⁢ ( 2 ⁢ j + λ - μ - 2 ) subscript 𝐾 𝑗 𝑗 𝛼 𝜇 1 𝑗 𝛽 𝜇 1 𝑗 𝛾 𝜇 1 𝑗 𝜆 1 2 𝑗 𝜆 𝜇 1 2 𝑗 𝜆 𝜇 2 {\displaystyle{\displaystyle K_{j}=-\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+% \gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}}}
K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}		 

K[j] = -((j + alpha - mu - 1)*(j + beta - mu - 1)*(j + gamma - mu - 1)*(j + lambda - 1))/((2*j + lambda - mu - 1)*(2*j + lambda - mu - 2))
 
Subscript[K, j] == -Divide[(j + \[Alpha]- \[Mu]- 1)*(j + \[Beta]- \[Mu]- 1)*(j + \[Gamma]- \[Mu]- 1)*(j + \[Lambda]- 1),(2*j + \[Lambda]- \[Mu]- 1)*(2*j + \[Lambda]- \[Mu]- 2)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E7 L j = a ⁢ ( λ + j ) ⁢ ( μ - j ) - q + ( j + α - μ ) ⁢ ( j + β - μ ) ⁢ ( j + γ - μ ) ⁢ ( j + λ ) ( 2 ⁢ j + λ - μ ) ⁢ ( 2 ⁢ j + λ - μ + 1 ) + ( j - α + λ ) ⁢ ( j - β + λ ) ⁢ ( j - γ + λ ) ⁢ ( j - μ ) ( 2 ⁢ j + λ - μ ) ⁢ ( 2 ⁢ j + λ - μ - 1 ) subscript 𝐿 𝑗 𝑎 𝜆 𝑗 𝜇 𝑗 𝑞 𝑗 𝛼 𝜇 𝑗 𝛽 𝜇 𝑗 𝛾 𝜇 𝑗 𝜆 2 𝑗 𝜆 𝜇 2 𝑗 𝜆 𝜇 1 𝑗 𝛼 𝜆 𝑗 𝛽 𝜆 𝑗 𝛾 𝜆 𝑗 𝜇 2 𝑗 𝜆 𝜇 2 𝑗 𝜆 𝜇 1 {\displaystyle{\displaystyle L_{j}=a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(% j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+% \frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+% \lambda-\mu)(2j+\lambda-\mu-1)}}}
L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}		 

L[j] = a*(lambda + j)*(mu - j)- q +((j + alpha - mu)*(j + beta - mu)*(j + gamma - mu)*(j + lambda))/((2*j + lambda - mu)*(2*j + lambda - mu + 1))+((j - alpha + lambda)*(j - beta + lambda)*(j - gamma + lambda)*(j - mu))/((2*j + lambda - mu)*(2*j + lambda - mu - 1))
 
Subscript[L, j] == a*(\[Lambda]+ j)*(\[Mu]- j)- q +Divide[(j + \[Alpha]- \[Mu])*(j + \[Beta]- \[Mu])*(j + \[Gamma]- \[Mu])*(j + \[Lambda]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]+ 1)]+Divide[(j - \[Alpha]+ \[Lambda])*(j - \[Beta]+ \[Lambda])*(j - \[Gamma]+ \[Lambda])*(j - \[Mu]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]- 1)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E8 M j = - ( j - α + λ + 1 ) ⁢ ( j - β + λ + 1 ) ⁢ ( j - γ + λ + 1 ) ⁢ ( j - μ + 1 ) ( 2 ⁢ j + λ - μ + 1 ) ⁢ ( 2 ⁢ j + λ - μ + 2 ) subscript 𝑀 𝑗 𝑗 𝛼 𝜆 1 𝑗 𝛽 𝜆 1 𝑗 𝛾 𝜆 1 𝑗 𝜇 1 2 𝑗 𝜆 𝜇 1 2 𝑗 𝜆 𝜇 2 {\displaystyle{\displaystyle M_{j}=-\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda% +1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}}}
M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}		 

M[j] = -((j - alpha + lambda + 1)*(j - beta + lambda + 1)*(j - gamma + lambda + 1)*(j - mu + 1))/((2*j + lambda - mu + 1)*(2*j + lambda - mu + 2))
 
Subscript[M, j] == -Divide[(j - \[Alpha]+ \[Lambda]+ 1)*(j - \[Beta]+ \[Lambda]+ 1)*(j - \[Gamma]+ \[Lambda]+ 1)*(j - \[Mu]+ 1),(2*j + \[Lambda]- \[Mu]+ 1)*(2*j + \[Lambda]- \[Mu]+ 2)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E9 M - 1 ⁢ P - 1 = 0 subscript 𝑀 1 subscript 𝑃 1 0 {\displaystyle{\displaystyle M_{-1}P_{-1}=0}}
M_{-1}P_{-1} = 0		 

M[- 1]*P[- 1] = 0
 
Subscript[M, - 1]*Subscript[P, - 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex1 λ = α 𝜆 𝛼 {\displaystyle{\displaystyle\lambda=\alpha}}
\lambda = \alpha		 

lambda = alpha
 
\[Lambda] == \[Alpha]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex2 μ = β - ϵ 𝜇 𝛽 italic-ϵ {\displaystyle{\displaystyle\mu=\beta-\epsilon}}
\mu = \beta-\epsilon		 

mu = beta - epsilon
 
\[Mu] == \[Beta]- \[Epsilon]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex3 λ = β 𝜆 𝛽 {\displaystyle{\displaystyle\lambda=\beta}}
\lambda = \beta		 

lambda = beta
 
\[Lambda] == \[Beta]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex4 μ = α - ϵ 𝜇 𝛼 italic-ϵ {\displaystyle{\displaystyle\mu=\alpha-\epsilon}}
\mu = \alpha-\epsilon		 

mu = alpha - epsilon
 
\[Mu] == \[Alpha]- \[Epsilon]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex5 λ = γ + δ - 1 𝜆 𝛾 𝛿 1 {\displaystyle{\displaystyle\lambda=\gamma+\delta-1}}
\lambda = \gamma+\delta-1		 

lambda = gamma + delta - 1
 
\[Lambda] == \[Gamma]+ \[Delta]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex6 μ = 0 𝜇 0 {\displaystyle{\displaystyle\mu=0}}
\mu = 0		 

mu = 0
 
\[Mu] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex7 λ = γ 𝜆 𝛾 {\displaystyle{\displaystyle\lambda=\gamma}}
\lambda = \gamma		 

lambda = gamma
 
\[Lambda] == \[Gamma]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex8 μ = δ - 1 𝜇 𝛿 1 {\displaystyle{\displaystyle\mu=\delta-1}}
\mu = \delta-1		 

mu = delta - 1
 
\[Mu] == \[Delta]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex9 λ = δ 𝜆 𝛿 {\displaystyle{\displaystyle\lambda=\delta}}
\lambda = \delta		 

lambda = delta
 
\[Lambda] == \[Delta]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex10 μ = γ - 1 𝜇 𝛾 1 {\displaystyle{\displaystyle\mu=\gamma-1}}
\mu = \gamma-1		 

mu = gamma - 1
 
\[Mu] == \[Gamma]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex11 λ = 1 𝜆 1 {\displaystyle{\displaystyle\lambda=1}}
\lambda = 1		 

lambda = 1
 
\[Lambda] == 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex12 μ = γ + δ - 2 𝜇 𝛾 𝛿 2 {\displaystyle{\displaystyle\mu=\gamma+\delta-2}}
\mu = \gamma+\delta-2		 

mu = gamma + delta - 2
 
\[Mu] == \[Gamma]+ \[Delta]- 2
 Skipped - no semantic math Skipped - no semantic math - -
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