Formula:6111

Digital Library of Mathematical Functions ID 17.7.E18

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

Symbols List

• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$: basic hypergeometric (or $$q$$ -hypergeometric) function
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle r}}$: nonnegative integer
 

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