Orthogonal Polynomials - 18.27 -Hahn Class
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.27.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A(x)p_{n}(qx)+B(x)p_{n}(x)+C(x)p_{n}(q^{-1}x) = \lambda_{n}p_{n}(x)}
A(x)p_{n}(qx)+B(x)p_{n}(x)+C(x)p_{n}(q^{-1}x) = \lambda_{n}p_{n}(x) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A(x)* p[n](q*x)+ B(x)* p[n](x)+ C(x)* p[n]((q)^(- 1)* x) = lambda[n]*p[n](x) |
A[x]* Subscript[p, n][q*x]+ B[x]* Subscript[p, n][x]+ C[x]* Subscript[p, n][(q)^(- 1)* x] == Subscript[\[Lambda], n]*Subscript[p, n][x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 18.27.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v_{x} = \frac{(a^{-1}x,c^{-1}x;q)_{\infty}}{(x,bc^{-1}x;q)_{\infty}}}
v_{x} = \frac{(a^{-1}x,c^{-1}x;q)_{\infty}}{(x,bc^{-1}x;q)_{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < a, a < q^{-1}, 0 < b, b < q^{-1}, c < 0} | v[x] = ((a)^(- 1)* x , (c)^(- 1)* x ; q[infinity])/(x , b*(c)^(- 1)* x ; q[infinity]) |
Subscript[v, x] == Divide[Subscript[(a)^(- 1)* x , (c)^(- 1)* x ; q, Infinity],Subscript[x , b*(c)^(- 1)* x ; q, Infinity]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 18.27.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v_{x} = \frac{(qx/c,-qx/d;q)_{\infty}}{(q^{\alpha+1}x/c,-q^{\beta+1}x/d;q)_{\infty}}}
v_{x} = \frac{(qx/c,-qx/d;q)_{\infty}}{(q^{\alpha+1}x/c,-q^{\beta+1}x/d;q)_{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha > -1, \beta > -1, c > 0, d > 0} | v[x] = (q*x/c , - q*x/d ; q[infinity])/((q)^(alpha + 1)* x/c , - (q)^(beta + 1)* x/d ; q[infinity]) |
Subscript[v, x] == Divide[Subscript[q*x/c , - q*x/d ; q, Infinity],Subscript[(q)^(\[Alpha]+ 1)* x/c , - (q)^(\[Beta]+ 1)* x/d ; q, Infinity]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 18.27.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{0}@@{q^{-n},q^{-n+1}}{-}{q^{2}}{x^{-2}q^{2n-1}}}
\qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{0}@@{q^{-n},q^{-n+1}}{-}{q^{2}}{x^{-2}q^{2n-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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QPochhammer[q, q, n]*Sum[Divide[(- 1)^\[ScriptL]* (q)^(\[ScriptL]*(\[ScriptL]- 1))* (x)^(n - 2*\[ScriptL]),QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[q, q, n - 2*\[ScriptL]]], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (x)^(n)* QHypergeometricPFQ[{(q)^(- n), (q)^(- n + 1)},{-},(q)^(2),(x)^(- 2)* (q)^(2*n - 1)]
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Missing Macro Error | Failure | - | Error |
| 18.27.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{-2n\ell}q^{\ell(2\ell+1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{1}@@{q^{-n},q^{-n+1}}{0}{q^{2}}{-x^{-2}q^{2}}}
\qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{-2n\ell}q^{\ell(2\ell+1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{1}@@{q^{-n},q^{-n+1}}{0}{q^{2}}{-x^{-2}q^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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QPochhammer[q, q, n]*Sum[Divide[(- 1)^\[ScriptL]* (q)^(- 2*n*\[ScriptL])* (q)^(\[ScriptL]*(2*\[ScriptL]+ 1))* (x)^(n - 2*\[ScriptL]),QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[q, q, n - 2*\[ScriptL]]], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (x)^(n)* QHypergeometricPFQ[{(q)^(- n), (q)^(- n + 1)},{0},(q)^(2),- (x)^(- 2)* (q)^(2)]
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Missing Macro Error | Aborted | - | Skipped - Because timed out |