DLMF:20.4.E11 (Q6766)

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DLMF:20.4.E11
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    Statements

    Defining formula
    θ 4 ′′ ⁡ ( 0 , q ) θ 4 ⁡ ( 0 , q ) = 8 ⁢ ∑ n = 1 ∞ q 2 ⁢ n - 1 ( 1 - q 2 ⁢ n - 1 ) 2 . diffop Jacobi-theta 4 2 0 𝑞 Jacobi-theta 4 0 𝑞 8 superscript subscript 𝑛 1 superscript 𝑞 2 𝑛 1 superscript 1 superscript 𝑞 2 𝑛 1 2 {\displaystyle{\displaystyle\frac{\theta_{4}''\left(0,q\right)}{\theta_{4}% \left(0,q\right)}=8\sum_{n=1}^{\infty}\frac{q^{2n-1}}{(1-q^{2n-1})^{2}}.}}
    0 references
    DLMF id
    DLMF:20.4.E11
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2ajdec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1gdec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1jdec
    0 references
     
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