q -Hypergeometric and Related Functions - 17.5 Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 17.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{0}{0}@{-}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}}}
\qgenhyperphi{0}{0}@{-}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | Error
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QHypergeometricPFQ[{-},{-},q,z] == Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]
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Missing Macro Error | Failure | Skip - symbolical successful subtest | Error |
| 17.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{z}{q}{\infty}}
\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{z}{q}{\infty} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | sum(((- 1)^(n)* (q)^(binomial(n,2))* (z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(z, q, infinity)
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Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[z, q, Infinity]
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Failure | Failure | Error | Failed [8 / 10]
Result: Plus[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}
Result: Indeterminate
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}
... skip entries to safe data |
| 17.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{a}{-}{q}{z} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}}
\qgenhyperphi{1}{0}@{a}{-}{q}{z} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | Error
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QHypergeometricPFQ[{a},{-},q,z] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]]
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Missing Macro Error | Failure | - | Error |
| 17.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{q^{-n}}{-}{q}{z} = \qPochhammer{zq^{-n}}{q}{n}}
\qgenhyperphi{1}{0}@{q^{-n}}{-}{q}{z} = \qPochhammer{zq^{-n}}{q}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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QHypergeometricPFQ[{(q)^(- n)},{-},q,z] == QPochhammer[z*(q)^(- n), q, n]
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Missing Macro Error | Failure | - | Error |
| 17.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{0}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}}}
\qgenhyperphi{1}{0}@{0}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | Error
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QHypergeometricPFQ[{0},{-},q,z] == Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]
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Missing Macro Error | Failure | Skip - symbolical successful subtest | Error |
| 17.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{z}{q}{\infty}}}
\sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{z}{q}{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | sum(((z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer(z, q, infinity))
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Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, Infinity]]
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Failure | Failure | Error | Failed [8 / 10]
Result: Plus[QHypergeometricPFQ[{0.0}
Test Values: {}, Complex[0.8660254037844387, 0.49999999999999994], 0.5], Times[-1.0, Power[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}
Result: QHypergeometricPFQ[{0.0}
Test Values: {}, Complex[-0.4999999999999998, 0.8660254037844387], 0.5], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}
... skip entries to safe data |
| 17.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{1}@@{a}{c}{q}{c/a} = \frac{\qPochhammer{c/a}{q}{\infty}}{\qPochhammer{c}{q}{\infty}}}
\qgenhyperphi{1}{1}@@{a}{c}{q}{c/a} = \frac{\qPochhammer{c/a}{q}{\infty}}{\qPochhammer{c}{q}{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |c| < |a|} | Error
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QHypergeometricPFQ[{a},{c},q,c/a] == Divide[QPochhammer[c/a, q, Infinity],QPochhammer[c, q, Infinity]]
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Missing Macro Error | Failure | - | Failed [96 / 120]
Result: Plus[QHypergeometricPFQ[{-1.5}
Test Values: {-0.5}, Complex[0.8660254037844387, 0.49999999999999994], 0.3333333333333333], Times[-1.0, Power[QPochhammer[-0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[0.3333333333333333, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |