DLMF:20.7.E23 (Q6818)

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DLMF:20.7.E23
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    Statements

    Defining formula
    θ 3 ⁡ ( 4 ⁢ z | 4 ⁢ τ ) = B ⁢ θ 3 ⁡ ( 1 8 ⁢ π - z | τ ) ⁢ θ 3 ⁡ ( 1 8 ⁢ π + z | τ ) ⁢ θ 3 ⁡ ( 3 8 ⁢ π - z | τ ) ⁢ θ 3 ⁡ ( 3 8 ⁢ π + z | τ ) , Jacobi-theta-tau 3 4 𝑧 4 𝜏 𝐵 Jacobi-theta-tau 3 1 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 3 1 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 3 3 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 3 3 8 𝜋 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{3}\left(4z\middle|4\tau\right)=B\theta_{3}% \left(\tfrac{1}{8}\pi-z\middle|\tau\right)\theta_{3}\left(\tfrac{1}{8}\pi+z% \middle|\tau\right)\*\theta_{3}\left(\tfrac{3}{8}\pi-z\middle|\tau\right)% \theta_{3}\left(\tfrac{3}{8}\pi+z\middle|\tau\right),}}
    0 references
    DLMF id
    DLMF:20.7.E23
    0 references
    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.m1ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1sdec
    0 references
     
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