DLMF:20.7.E31 (Q6826)

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DLMF:20.7.E31
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    Statements

    Defining formula
    ( - i ⁢ τ ) 1 / 2 ⁢ θ 2 ⁡ ( z | τ ) = exp ⁡ ( i ⁢ τ ′ ⁢ z 2 / π ) ⁢ θ 4 ⁡ ( z ⁢ τ ′ | τ ′ ) , superscript 𝑖 𝜏 1 2 Jacobi-theta-tau 2 𝑧 𝜏 𝑖 superscript 𝜏 ′ superscript 𝑧 2 𝜋 Jacobi-theta-tau 4 𝑧 superscript 𝜏 ′ superscript 𝜏 ′ {\displaystyle{\displaystyle(-i\tau)^{1/2}\theta_{2}\left(z\middle|\tau\right)% =\exp\left(i\tau^{\prime}z^{2}/\pi\right)\theta_{4}\left(z\tau^{\prime}\middle% |\tau^{\prime}\right),}}
    0 references
    DLMF id
    DLMF:20.7.E31
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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.m1apdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1aadec
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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1pdec
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