q -Hypergeometric and Related Functions - 17.3 -Elementary and -Special Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
17.3.E1	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left((1-q)x;q\right)_{\infty}}}}$ \sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}		sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)*x, q, infinity))	Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)*x, q, Infinity]]	Failure	Aborted	Error	Skipped - Because timed out
17.3.E2	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}x^{n}}{\left(q;q\right)_{n}}=\left(-(1-q)x;q\right)_{\infty}}}$ \sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}		sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)*x, q, infinity)	Sum[Divide[(1 - q)^(n)* (q)^(Binomial[n,2])* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[-(1 - q)*x, q, Infinity]	Failure	Aborted	Error	Skipped - Because timed out