Formula:6164

Digital Library of Mathematical Functions ID 17.13.E2

${\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}\left(qx/d;q\right)_{\infty}}{\left(-xq^{\alpha}/c;q\right)_{\infty}\left(xq^{\beta}/d;q\right)_{\infty}}{\mathrm{d}}_{q}x=\frac{\Gamma_{q}\left(\alpha\right)\Gamma_{q}\left(\beta\right)}{\Gamma_{q}\left(\alpha+\beta\right)}\frac{cd}{c+d}\frac{\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{\left(-q^{\beta}c/d;q\right)_{\infty}\left(-q^{\alpha}d/c;q\right)_{\infty}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}$: $$q$$ -gamma function
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.