Formula:6152

Digital Library of Mathematical Functions ID 17.11.E3

${\displaystyle{\displaystyle\Phi^{(3)}\left(a,a^{\prime};b,b^{\prime};c;q;x,y\right)=\frac{\left(a,bx;q\right)_{\infty}}{\left(c,x;q\right)_{\infty}}\sum_{n,r\geqq 0}\frac{\left(a^{\prime},b^{\prime};q\right)_{n}\left(x;q\right)_{r}\left(c/a;q\right)_{n+r}a^{r}y^{n}}{\left(q,c/a;q\right)_{n}\left(q,bx;q\right)_{r}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\Phi^{(3)}\left(\NVar{a},\NVar{a^{\prime}};\NVar{b},\NVar{b^{\prime}};;missing;missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$: third $$q$$ -Appell function
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle r}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
 

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