Formula:6153

Digital Library of Mathematical Functions ID 17.11.E4

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

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
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.