17.5

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
17.5.E1	${\displaystyle{\displaystyle{{}_{0}\phi_{0}}\left(-;-;q,z\right)=\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}z^{n}}{\left(q;q\right)_{n}}}}$ \qgenhyperphi{0}{0}@{-}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}}	${\displaystyle{\displaystyle|z|<1}}$	Error	QHypergeometricPFQ[{-},{-},q,z] == Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Failure	Skip - symbolical successful subtest	Error
17.5.E1	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}z^{n}}{\left(q;q\right)_{n}}=\left(z;q\right)_{\infty}}}$ \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{z}{q}{\infty}	${\displaystyle{\displaystyle|z|<1}}$	sum(((- 1)^(n)* (q)^(binomial(n,2))* (z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(z, q, infinity)	Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[z, q, Infinity]	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	${\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(a;-;q,z\right)=\frac{\left(az;q\right)_{\infty}}{\left(z;q\right)_{\infty}}}}$ \qgenhyperphi{1}{0}@{a}{-}{q}{z} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}	${\displaystyle{\displaystyle|z|<1}}$	Error	QHypergeometricPFQ[{a},{-},q,z] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]]	Missing Macro Error	Failure	-	Error
17.5.E3	${\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(q^{-n};-;q,z\right)=\left(zq^{-n};q\right)_{n}}}$ \qgenhyperphi{1}{0}@{q^{-n}}{-}{q}{z} = \qPochhammer{zq^{-n}}{q}{n}		Error	QHypergeometricPFQ[{(q)^(- n)},{-},q,z] == QPochhammer[z*(q)^(- n), q, n]	Missing Macro Error	Failure	-	Error
17.5.E4	${\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(0;-;q,z\right)=\sum_{n=0}^{\infty}\frac{z^{n}}{\left(q;q\right)_{n}}}}$ \qgenhyperphi{1}{0}@{0}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}}	${\displaystyle{\displaystyle|z|<1}}$	Error	QHypergeometricPFQ[{0},{-},q,z] == Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Failure	Skip - symbolical successful subtest	Error
17.5.E4	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{z^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left(z;q\right)_{\infty}}}}$ \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{z}{q}{\infty}}	${\displaystyle{\displaystyle|z|<1}}$	sum(((z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer(z, q, infinity))	Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, Infinity]]	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	${\displaystyle{\displaystyle{{}_{1}\phi_{1}}\left({a\atop c};q,c/a\right)=\frac{\left(c/a;q\right)_{\infty}}{\left(c;q\right)_{\infty}}}}$ \qgenhyperphi{1}{1}@@{a}{c}{q}{c/a} = \frac{\qPochhammer{c/a}{q}{\infty}}{\qPochhammer{c}{q}{\infty}}	${\displaystyle{\displaystyle|c|<|a|}}$	Error	QHypergeometricPFQ[{a},{c},q,c/a] == Divide[QPochhammer[c/a, q, Infinity],QPochhammer[c, q, Infinity]]	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