DLMF:17.3.E1 (Q5341)

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DLMF:17.3.E1
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    Statements

    Defining formula
    e q ⁡ ( x ) = ∑ n = 0 ∞ ( 1 - q ) n ⁢ x n ( q ; q ) n = 1 ( ( 1 - q ) ⁢ x ; q ) ∞ , q-exp 𝑞 𝑥 superscript subscript 𝑛 0 superscript 1 𝑞 𝑛 superscript 𝑥 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 1 q-Pochhammer-symbol 1 𝑞 𝑥 𝑞 {\displaystyle{\displaystyle e_{q}\left(x\right)=\sum_{n=0}^{\infty}\frac{(1-q% )^{n}x^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left((1-q)x;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.3.E1
    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.m2adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1dec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1dec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1dec
    0 references
     
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