DLMF:17.2.E34 (Q5324)

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DLMF:17.2.E34
No description defined

    Statements

    Defining formula
    lim n → ∞ ⁡ [ r ⁢ n + u s ⁢ n + t ] q = 1 ( q ; q ) ∞ = ∏ j = 1 ∞ 1 ( 1 - q j ) , subscript → 𝑛 q-binomial 𝑟 𝑛 𝑢 𝑠 𝑛 𝑡 𝑞 1 q-Pochhammer-symbol 𝑞 𝑞 superscript subscript product 𝑗 1 1 1 superscript 𝑞 𝑗 {\displaystyle{\displaystyle\lim_{n\to\infty}\genfrac{[}{]}{0.0pt}{}{rn+u}{sn+% t}_{q}=\frac{1}{\left(q;q\right)_{\infty}}=\prod_{j=1}^{\infty}\frac{1}{(1-q^{% j})},}}
    0 references
    DLMF id
    DLMF:17.2.E34
    0 references
    Symbols used
    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.m2aacdec
    0 references
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    Defining formula
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2agdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1agdec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1ddec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1addec
    0 references
    Q11714
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C17.S1.XMD5.m1bdec
    0 references
    Q11717
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C17.S1.XMD6.m1dec
    0 references
     
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