DLMF:17.6.E9 (Q5376)

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Language	Label	Description	Also known as
English	DLMF:17.6.E9	No description defined

Statements

Defining formula

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

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DLMF:17.6.E9

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

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2aedec

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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.m2ahdec

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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.m6aedec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1hdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1bdec

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