DLMF:17.6.E28 (Q5395)

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Language	Label	Description	Also known as
English	DLMF:17.6.E28	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q^{\alpha},q^{\beta}\atop q% ^{\gamma}};q,z\right)=\frac{\Gamma_{q}\left(\gamma\right)}{\Gamma_{q}\left(% \beta\right)\Gamma_{q}\left(\gamma-\beta\right)}\int_{0}^{1}\frac{t^{\beta-1}% \left(tq;q\right)_{\gamma-\beta-1}}{\left(xt;q\right)_{\alpha}}{\mathrm{d}}_{q% }t.}}

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DLMF:17.6.E28

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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$$q$$ -gamma function

Defining formula

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

C5.S18.E4.m2adec

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Defining formula

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

C17.S2.SS1.p1.m2akdec

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Defining formula

{\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}

C17.S2.SS5.p1.m3adec

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basic hypergeometric (or $$q$$ -hypergeometric) function

Defining formula

{\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)}}

C17.S4.E1.m2aaadec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1aadec

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Defining formula

{\displaystyle{\displaystyle z}}

C17.S1.XMD7.m1udec

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Defining formula

{\displaystyle{\displaystyle x}}

C17.S1.XMD8.m1dec

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