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DLMF:17.12.E4 - MaRDI portal

DLMF:17.12.E4 (Q6158)

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DLMF:17.12.E4
No description defined

    Statements

    DLMF defining formula
    ∑ n = 0 ∞ q n 2 ⁢ a n ⁢ β n = 1 ( a ⁢ q ; q ) ∞ ⁢ ∑ n = 0 ∞ q n 2 ⁢ a n ⁢ α n . superscript subscript 𝑛 0 superscript 𝑞 superscript 𝑛 2 superscript 𝑎 𝑛 subscript 𝛽 𝑛 1 q-Pochhammer-symbol 𝑎 𝑞 𝑞 superscript subscript 𝑛 0 superscript 𝑞 superscript 𝑛 2 superscript 𝑎 𝑛 subscript 𝛼 𝑛 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\beta_{n}=\frac{1% }{\left(aq;q\right)_{\infty}}\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\alpha_{n}.}}
    0 references
    Symbols used
    Q11269
    DLMF 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
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1cdec
    0 references
    part of Bailey pair
    DLMF defining formula
    α n subscript 𝛼 𝑛 {\displaystyle{\displaystyle\alpha_{n}}}
    xml-id
    C17.S12.XMD1.m1cdec
    0 references
    part of Bailey pair
    DLMF defining formula
    β n subscript 𝛽 𝑛 {\displaystyle{\displaystyle\beta_{n}}}
    xml-id
    C17.S12.XMD2.m1cdec
    0 references

    Identifiers

     
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