DLMF:17.6.E28 (Q5395)

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DLMF:17.6.E28
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    Statements

    Defining formula
    ϕ 1 2 ⁡ ( q α , q β q γ ; q , z ) = Γ q ⁡ ( γ ) Γ q ⁡ ( β ) ⁢ Γ q ⁡ ( γ - β ) ⁢ ∫ 0 1 t β - 1 ⁢ ( t ⁢ q ; q ) γ - β - 1 ( x ⁢ t ; q ) α ⁢ d q t . q-hypergeometric-rphis 2 1 superscript 𝑞 𝛼 superscript 𝑞 𝛽 superscript 𝑞 𝛾 𝑞 𝑧 q-Gamma 𝑞 𝛾 q-Gamma 𝑞 𝛽 q-Gamma 𝑞 𝛾 𝛽 superscript subscript 0 1 superscript 𝑡 𝛽 1 q-Pochhammer-symbol 𝑡 𝑞 𝑞 𝛾 𝛽 1 q-Pochhammer-symbol 𝑥 𝑡 𝑞 𝛼 q-differential 𝑞 𝑡 {\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 id
    DLMF:17.6.E28
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