DLMF:17.2.E13 (Q5303)

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DLMF:17.2.E13
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    Statements

    Defining formula
    ( a ; q ) n - k = ( a ; q ) n ( q 1 - n / a ; q ) k ⁢ ( - q a ) k ⁢ q ( k 2 ) - n ⁢ k , q-Pochhammer-symbol 𝑎 𝑞 𝑛 𝑘 q-Pochhammer-symbol 𝑎 𝑞 𝑛 q-Pochhammer-symbol superscript 𝑞 1 𝑛 𝑎 𝑞 𝑘 superscript 𝑞 𝑎 𝑘 superscript 𝑞 binomial 𝑘 2 𝑛 𝑘 {\displaystyle{\displaystyle\left(a;q\right)_{n-k}=\frac{\left(a;q\right)_{n}}% {\left(q^{1-n}/a;q\right)_{k}}\left(-\frac{q}{a}\right)^{k}q^{\genfrac{(}{)}{0% .0pt}{}{k}{2}-nk},}}
    0 references
    DLMF id
    DLMF:17.2.E13
    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.m1addec
    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.m2aldec
    0 references
    Q11715
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1dec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ldec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1idec
    0 references
     
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