DLMF:17.7.E18 (Q5414)

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Language	Label	Description	Also known as
English	DLMF:17.7.E18	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{r+2}\phi_{r+1}}\left({a,b,b_{1}q^{m_{1}},% \dots,b_{r}q^{m_{r}}\atop bq,b_{1},\dots,b_{r}};q,a^{-1}q^{1-(m_{1}+\cdots+m_{% r})}\right)=\frac{\left(q,bq/a;q\right)_{\infty}\left(b_{1}/b;q\right)_{m_{1}}% \cdots\left(b_{r}/b;q\right)_{m_{r}}}{\left(bq,q/a;q\right)_{\infty}\left(b_{1% };q\right)_{m_{1}}\cdots\left(b_{r};q\right)_{m_{r}}}b^{m_{1}+\cdots+m_{r}},}}

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DLMF:17.7.E18

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Defining formula

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

C17.S2.SS1.p1.m2abdec

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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.m2aqdec

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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.m6aqdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1qdec

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Defining formula

{\displaystyle{\displaystyle m}}

C17.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle r}}

C17.S1.XMD5.m1dec

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