DLMF:17.2.E25 (Q5315)

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DLMF:17.2.E25
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    Statements

    test
    lim τ → 0 ⁡ ( a / τ ; q ) n ( b / τ ; q ) n = lim σ → ∞ ⁡ ( a ⁢ σ ; q ) n ( b ⁢ σ ; q ) n = ( a b ) n , subscript → 𝜏 0 q-Pochhammer-symbol 𝑎 𝜏 𝑞 𝑛 q-Pochhammer-symbol 𝑏 𝜏 𝑞 𝑛 subscript → 𝜎 q-Pochhammer-symbol 𝑎 𝜎 𝑞 𝑛 q-Pochhammer-symbol 𝑏 𝜎 𝑞 𝑛 superscript 𝑎 𝑏 𝑛 {\displaystyle{\displaystyle\lim_{\tau\to 0}\frac{\left(a/\tau;q\right)_{n}}{% \left(b/\tau;q\right)_{n}}=\lim_{\sigma\to\infty}\frac{\left(a\sigma;q\right)_% {n}}{\left(b\sigma;q\right)_{n}}=\left(\frac{a}{b}\right)^{n},}}
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    DLMF id
    DLMF:17.2.E25
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