DLMF:17.11.E4 (Q5456)

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Language	Label	Description	Also known as
English	DLMF:17.11.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{m_{1},\dots,m_{n}\geqq 0}\frac{\left(a;q% \right)_{m_{1}+m_{2}+\cdots+m_{n}}\left(b_{1};q\right)_{m_{1}}\left(b_{2};q% \right)_{m_{2}}\cdots\left(b_{n};q\right)_{m_{n}}x_{1}^{m_{1}}x_{2}^{m_{2}}% \cdots x_{n}^{m_{n}}}{\left(q;q\right)_{m_{1}}\left(q;q\right)_{m_{2}}\cdots% \left(q;q\right)_{m_{n}}\left(c;q\right)_{m_{1}+m_{2}+\cdots+m_{n}}}=\frac{% \left(a,b_{1}x_{1},b_{2}x_{2},\dots,b_{n}x_{n};q\right)_{\infty}}{\left(c,x_{1% },x_{2},\dots,x_{n};q\right)_{\infty}}{{}_{n+1}\phi_{n}}\left({c/a,x_{1},x_{2}% ,\dots,x_{n}\atop b_{1}x_{1},b_{2}x_{2},\dots,b_{n}x_{n}};q,a\right).}}

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DLMF:17.11.E4

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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.m2aadec

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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 m}}

C17.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle x}}

C17.S1.XMD8.m1cdec

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