DLMF:20.6.E5 (Q6789)

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DLMF:20.6.E5
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    Statements

    Defining formula
    θ 4 ⁡ ( π ⁢ z | τ ) = θ 4 ⁡ ( 0 | τ ) ⁢ exp ⁡ ( - ∑ j = 1 ∞ 1 2 ⁢ j ⁢ γ 2 ⁢ j ⁢ ( τ ) ⁢ z 2 ⁢ j ) . Jacobi-theta-tau 4 𝜋 𝑧 𝜏 Jacobi-theta-tau 4 0 𝜏 superscript subscript 𝑗 1 1 2 𝑗 subscript 𝛾 2 𝑗 𝜏 superscript 𝑧 2 𝑗 {\displaystyle{\displaystyle\theta_{4}\left(\pi z\middle|\tau\right)=\theta_{4% }\left(0\middle|\tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\gamma_{2% j}(\tau)z^{2j}\right).}}
    0 references
    DLMF id
    DLMF:20.6.E5
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    Symbols used
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2acdec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1ddec
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