DLMF:20.5.E4 (Q6771)

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DLMF:20.5.E4
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    Statements

    Defining formula
    θ 4 ⁡ ( z , q ) = ∏ n = 1 ∞ ( 1 - q 2 ⁢ n ) ⁢ ( 1 - 2 ⁢ q 2 ⁢ n - 1 ⁢ cos ⁡ ( 2 ⁢ z ) + q 4 ⁢ n - 2 ) . Jacobi-theta 4 𝑧 𝑞 superscript subscript product 𝑛 1 1 superscript 𝑞 2 𝑛 1 2 superscript 𝑞 2 𝑛 1 2 𝑧 superscript 𝑞 4 𝑛 2 {\displaystyle{\displaystyle\theta_{4}\left(z,q\right)=\prod\limits_{n=1}^{% \infty}\left(1-q^{2n}\right)\left(1-2q^{2n-1}\cos\left(2z\right)+q^{4n-2}% \right).}}
    0 references
    DLMF id
    DLMF:20.5.E4
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    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.m2acdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1cdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1cdec
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