Formula:6150

Digital Library of Mathematical Functions ID 17.11.E1

${\displaystyle{\displaystyle\Phi^{(1)}\left(a;b,b^{\prime};c;q;x,y\right)=\frac{\left(a,bx,b^{\prime}y;q\right)_{\infty}}{\left(c,x,y;q\right)_{\infty}}{{}_{3}\phi_{2}}\left({c/a,x,y\atop bx,b^{\prime}y};q,a\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Phi^{(1)}\left(\NVar{a};\NVar{b},\NVar{b^{\prime}};\NVar{c};\NVar{q};,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$: first $$q$$ -Appell function
• ${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$: 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
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
 

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