DLMF:17.10.E4 (Q5450)

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Language	Label	Description	Also known as
English	DLMF:17.10.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{2}\psi_{2}}\left({e,f\atop aq/c,aq/d};q,\frac% {aq}{ef}\right)=\frac{\left(q/c,q/d,aq/e,aq/f;q\right)_{\infty}}{\left(aq,q/a,% aq/(cd),aq/(ef);q\right)_{\infty}}\*\sum_{n=-\infty}^{\infty}\frac{(1-aq^{2n})% \left(c,d,e,f;q\right)_{n}}{(1-a)\left(aq/c,aq/d,aq/e,aq/f;q\right)_{n}}\left(% \frac{qa^{3}}{cdef}\right)^{n}q^{n^{2}}.}}

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DLMF:17.10.E4

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bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E3.m2acdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6acdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1adec

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