DLMF:17.13.E2 (Q5467): Difference between revisions

Revision as of 15:10, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:17.13.E2	No description defined

{\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}}.}}

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DLMF:17.13.E2

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{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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{\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}

C5.S18.E4.m2adec

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{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2aadec

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@@ Property / Symbols used @@
+Q11298
@@ Property / Symbols used: Q11298 / rank @@
+Normal rank
@@ Property / Symbols used: Q11298 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$ 
\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
@@ Property / Symbols used: Q11298 / qualifier @@
+xml-id: C17.S2.SS1.p1.m2aadec