DLMF:17.13.E1 (Q5466)

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DLMF:17.13.E1
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    Statements

    - c d ( - q x / c ; q ) ( q x / d ; q ) ( - a x / c ; q ) ( b x / d ; q ) d q x = ( 1 - q ) ( q ; q ) ( a b ; q ) c d ( - c / d ; q ) ( - d / c ; q ) ( a ; q ) ( b ; q ) ( c + d ) ( - b c / d ; q ) ( - a d / c ; q ) , superscript subscript 𝑐 𝑑 q-Pochhammer-symbol 𝑞 𝑥 𝑐 𝑞 q-Pochhammer-symbol 𝑞 𝑥 𝑑 𝑞 q-Pochhammer-symbol 𝑎 𝑥 𝑐 𝑞 q-Pochhammer-symbol 𝑏 𝑥 𝑑 𝑞 q-differential 𝑞 𝑥 1 𝑞 q-Pochhammer-symbol 𝑞 𝑞 q-Pochhammer-symbol 𝑎 𝑏 𝑞 𝑐 𝑑 q-Pochhammer-symbol 𝑐 𝑑 𝑞 q-Pochhammer-symbol 𝑑 𝑐 𝑞 q-Pochhammer-symbol 𝑎 𝑞 q-Pochhammer-symbol 𝑏 𝑞 𝑐 𝑑 q-Pochhammer-symbol 𝑏 𝑐 𝑑 𝑞 q-Pochhammer-symbol 𝑎 𝑑 𝑐 𝑞 {\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}% \left(qx/d;q\right)_{\infty}}{\left(-ax/c;q\right)_{\infty}\left(bx/d;q\right)% _{\infty}}{\mathrm{d}}_{q}x=\frac{(1-q)\left(q;q\right)_{\infty}\left(ab;q% \right)_{\infty}cd\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{% \left(a;q\right)_{\infty}\left(b;q\right)_{\infty}(c+d)\left(-bc/d;q\right)_{% \infty}\left(-ad/c;q\right)_{\infty}},}}
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    DLMF:17.13.E1
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