DLMF:20.4.E9 (Q6764)

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DLMF:20.4.E9
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    Statements

    Defining formula
    θ 2 ′′ ⁡ ( 0 , q ) θ 2 ⁡ ( 0 , q ) = - 1 - 8 ⁢ ∑ n = 1 ∞ q 2 ⁢ n ( 1 + q 2 ⁢ n ) 2 , diffop Jacobi-theta 2 2 0 𝑞 Jacobi-theta 2 0 𝑞 1 8 superscript subscript 𝑛 1 superscript 𝑞 2 𝑛 superscript 1 superscript 𝑞 2 𝑛 2 {\displaystyle{\displaystyle\frac{\theta_{2}''\left(0,q\right)}{\theta_{2}% \left(0,q\right)}=-1-8\sum_{n=1}^{\infty}\frac{q^{2n}}{(1+q^{2n})^{2}},}}
    0 references
    DLMF id
    DLMF:20.4.E9
    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.m2ahdec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1edec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1hdec
    0 references
     
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