DLMF:17.6.E11 (Q5378)

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Language	Label	Description	Also known as
English	DLMF:17.6.E11	No description defined

Statements

Defining formula

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

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DLMF:17.6.E11

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

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Defining formula

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

C17.S2.SS1.p1.m2agdec

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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.m2ajdec

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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.m6agdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1jdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle z}}

C17.S1.XMD7.m1edec

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