DLMF:17.13.E4 (Q5469)

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Language	Label	Description	Also known as
English	DLMF:17.13.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}\frac{\left(-ctq^{% \alpha+\beta};q\right)_{\infty}}{\left(-ct;q\right)_{\infty}}{\mathrm{d}}_{q}t% =\frac{\Gamma_{q}\left(\alpha\right)\Gamma_{q}\left(\beta\right)\left(-cq^{% \alpha};q\right)_{\infty}\left(-q^{1-\alpha}/c;q\right)_{\infty}}{\Gamma_{q}% \left(\alpha+\beta\right)\left(-c;q\right)_{\infty}\left(-q/c;q\right)_{\infty% }}.}}

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DLMF:17.13.E4

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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$$q$$ -gamma function

Defining formula

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

C5.S18.E4.m2abdec

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Defining formula

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

C17.S2.SS1.p1.m2acdec

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