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DLMF:17.8.E1 - MaRDI portal

DLMF:17.8.E1 (Q6117)

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DLMF:17.8.E1
No description defined

    Statements

    DLMF defining formula
    ∑ n = - ∞ ∞ ( - z ) n ⁢ q n ⁢ ( n - 1 ) / 2 = ( q , z , q / z ; q ) ∞ ; superscript subscript 𝑛 superscript 𝑧 𝑛 superscript 𝑞 𝑛 𝑛 1 2 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2}=% \left(q,z,q/z;q\right)_{\infty};}}
    0 references
    Symbols used
    Q11684
    DLMF defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6adec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1dec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1dec
    0 references

    Identifiers

     
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