DLMF:17.6.E12 (Q5379)

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Language	Label	Description	Also known as
English	DLMF:17.6.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(1-z){{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z% \right)=\sum_{n=0}^{\infty}\frac{\left(aq,azq/b;q\right)_{n}}{\left(bq,zq;q% \right)_{n}}(1-azq^{2n+1})(bz)^{n}q^{n^{2}},}}

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DLMF:17.6.E12

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{\displaystyle{\displaystyle|z|<1}}

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

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E1.m2akdec

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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.m6ahdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1kdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle z}}

C17.S1.XMD7.m1fdec

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