DLMF:5.18.E12 (Q2199)

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DLMF:5.18.E12
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    Statements

    test
    B q ⁡ ( a , b ) = ∫ 0 1 t a - 1 ⁢ ( t ⁢ q ; q ) ∞ ( t ⁢ q b ; q ) ∞ ⁢ d q t , q-Beta 𝑞 𝑎 𝑏 superscript subscript 0 1 superscript 𝑡 𝑎 1 q-Pochhammer-symbol 𝑡 𝑞 𝑞 q-Pochhammer-symbol 𝑡 superscript 𝑞 𝑏 𝑞 q-differential 𝑞 𝑡 {\displaystyle{\displaystyle\mathrm{B}_{q}\left(a,b\right)=\int_{0}^{1}\frac{t% ^{a-1}\left(tq;q\right)_{\infty}}{\left(tq^{b};q\right)_{\infty}}{\mathrm{d}}_% {q}t,}}
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    DLMF id
    DLMF:5.18.E12
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
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    0 < q < 1 0 𝑞 1 {\displaystyle{\displaystyle 0<q<1}}
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    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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