DLMF:17.2.E24 (Q5314)

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DLMF:17.2.E24
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    Statements

    test
    lim τ → 0 ⁡ ( a / τ ; q ) n ⁢ τ n = lim σ → ∞ ⁡ ( a ⁢ σ ; q ) n ⁢ σ - n = ( - a ) n ⁢ q ( n 2 ) , subscript → 𝜏 0 q-Pochhammer-symbol 𝑎 𝜏 𝑞 𝑛 superscript 𝜏 𝑛 subscript → 𝜎 q-Pochhammer-symbol 𝑎 𝜎 𝑞 𝑛 superscript 𝜎 𝑛 superscript 𝑎 𝑛 superscript 𝑞 binomial 𝑛 2 {\displaystyle{\displaystyle\lim_{\tau\to 0}\left(a/\tau;q\right)_{n}\tau^{n}=% \lim_{\sigma\to\infty}\left(a\sigma;q\right)_{n}\sigma^{-n}=(-a)^{n}q^{% \genfrac{(}{)}{0.0pt}{}{n}{2}},}}
    0 references
    DLMF id
    DLMF:17.2.E24
    0 references
    Symbols used
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1afdec
    0 references
     
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