Formula:6053

Digital Library of Mathematical Functions ID 17.4.E7

${\displaystyle{\displaystyle\Phi^{(3)}\left(a,a^{\prime};b,b^{\prime};c;q;x,y\right)=\sum_{m,n\geq 0}\frac{\left(a,b;q\right)_{m}\left(a^{\prime},b^{\prime};q\right)_{n}x^{m}y^{n}}{\left(q;q\right)_{m}\left(q;q\right)_{n}\left(c;q\right)_{m+n}},}}$

Symbols List

• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
 

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