DLMF:17.3.E2 (Q5342)

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DLMF:17.3.E2
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    Statements

    Defining formula
    E q ⁡ ( x ) = ∑ n = 0 ∞ ( 1 - q ) n ⁢ q ( n 2 ) ⁢ x n ( q ; q ) n = ( - ( 1 - q ) ⁢ x ; q ) ∞ . q-Exp 𝑞 𝑥 superscript subscript 𝑛 0 superscript 1 𝑞 𝑛 superscript 𝑞 binomial 𝑛 2 superscript 𝑥 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 1 𝑞 𝑥 𝑞 {\displaystyle{\displaystyle E_{q}\left(x\right)=\sum_{n=0}^{\infty}\frac{(1-q% )^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}x^{n}}{\left(q;q\right)_{n}}=\left(-(1-q% )x;q\right)_{\infty}.}}
    0 references
    DLMF id
    DLMF:17.3.E2
    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.m1adec
    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.m2aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1adec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1adec
    0 references
     
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