DLMF:17.2.E26 (Q5316)

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DLMF:17.2.E26
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    Statements

    Defining formula
    lim τ → 0 ⁡ ( a / τ ; q ) n ⁢ ( b / τ ; q ) n ( c / τ 2 ; q ) n = ( - 1 ) n ⁢ ( a ⁢ b c ) n ⁢ q ( n 2 ) . subscript → 𝜏 0 q-Pochhammer-symbol 𝑎 𝜏 𝑞 𝑛 q-Pochhammer-symbol 𝑏 𝜏 𝑞 𝑛 q-Pochhammer-symbol 𝑐 superscript 𝜏 2 𝑞 𝑛 superscript 1 𝑛 superscript 𝑎 𝑏 𝑐 𝑛 superscript 𝑞 binomial 𝑛 2 {\displaystyle{\displaystyle\lim_{\tau\to 0}\frac{\left(a/\tau;q\right)_{n}% \left(b/\tau;q\right)_{n}}{\left(c/\tau^{2};q\right)_{n}}=(-1)^{n}\left(\frac{% ab}{c}\right)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}.}}
    0 references
    DLMF id
    DLMF:17.2.E26
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1agdec
    0 references
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2aydec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ydec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1vdec
    0 references
     
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