DLMF:17.8.E3 (Q5422)

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DLMF:17.8.E3
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    Statements

    Defining formula
    ∑ n = - ∞ ∞ ( - 1 ) n ⁢ q n ⁢ ( 3 ⁢ n - 1 ) / 2 ⁢ z 3 ⁢ n ⁢ ( 1 + z ⁢ q n ) = ( q , - z , - q / z ; q ) ∞ ⁢ ( q ⁢ z 2 , q / z 2 ; q 2 ) ∞ . superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑞 𝑛 3 𝑛 1 2 superscript 𝑧 3 𝑛 1 𝑧 superscript 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 q-multiple-Pochhammer 𝑞 superscript 𝑧 2 𝑞 superscript 𝑧 2 superscript 𝑞 2 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3% n}(1+zq^{n})=\left(q,-z,-q/z;q\right)_{\infty}\left(qz^{2},q/{z^{2}};q^{2}% \right)_{\infty}.}}
    0 references
    DLMF id
    DLMF:17.8.E3
    0 references
    Symbols used
    Q11713
    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.m6abdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1bdec
    0 references
     
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