q -Hypergeometric and Related Functions - 18.1 Notation
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 18.1#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{z}{q}{0} = 1}
\qPochhammer{z}{q}{0} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | QPochhammer(z, q, 0) = 1
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QPochhammer[z, q, 0] == 1
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Successful | Successful | - | Successful [Tested: 70] |
| 18.1#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{z}{q}{\infty} = \prod_{j=0}^{\infty}(1-zq^{j})}
\qPochhammer{z}{q}{\infty} = \prod_{j=0}^{\infty}(1-zq^{j}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | QPochhammer(z, q, infinity) = product(1 - z*(q)^(j), j = 0..infinity)
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QPochhammer[z, q, Infinity] == Product[1 - z*(q)^(j), {j, 0, Infinity}, GenerateConditions->None]
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Failure | Failure | Error | Failed [56 / 70]
Result: Plus[Times[-1.0, QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Times[-1.0, QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 18.1.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{0}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x}}
\ultrasphpoly{0}{n}@{x} = \frac{2}{n}\ChebyshevpolyT{n}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | GegenbauerC(n, 0, x) = (2)/(n)*ChebyshevT(n, x)
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GegenbauerC[n, 0, x] == Divide[2,n]*ChebyshevT[n, x]
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Failure | Failure | Successful [Tested: 3] | Failed [3 / 3]
Result: -6.0
Test Values: {Rule[n, 3], Rule[x, 1.5]}
Result: 0.6666666666666666
Test Values: {Rule[n, 3], Rule[x, 0.5]}
... skip entries to safe data |
| 18.1.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{n}\ChebyshevpolyT{n}@{x} = \frac{2(n-1)!}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x}}
\frac{2}{n}\ChebyshevpolyT{n}@{x} = \frac{2(n-1)!}{\Pochhammersym{\tfrac{1}{2}}{n}}\JacobipolyP{-\frac{1}{2}}{-\frac{1}{2}}{n}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)/(n)*ChebyshevT(n, x) = (2*factorial(n - 1))/(pochhammer((1)/(2), n))*JacobiP(n, -(1)/(2), -(1)/(2), x)
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Divide[2,n]*ChebyshevT[n, x] == Divide[2*(n - 1)!,Pochhammer[Divide[1,2], n]]*JacobiP[n, -Divide[1,2], -Divide[1,2], x]
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Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 18.1.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \shiftJacobipolyG{n}@{p}{q}{x} = \frac{n!}{\Pochhammersym{n+p}{n}}\JacobipolyP{p-q}{q-1}{n}@{2x-1}}
\shiftJacobipolyG{n}@{p}{q}{x} = \frac{n!}{\Pochhammersym{n+p}{n}}\JacobipolyP{p-q}{q-1}{n}@{2x-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | JacobiP(n, p-q, q-1, 2*(x)-1)*((n)!)/pochhammer(n+p, n) = (factorial(n))/(pochhammer(n + p, n))*JacobiP(n, p - q, q - 1, 2*x - 1)
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Error
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Successful | Missing Macro Error | - | - |