DLMF:20.2.E12 (Q6752)

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DLMF:20.2.E12
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    Statements

    Defining formula
    θ 2 ⁡ ( z | τ ) = θ 1 ⁡ ( z + 1 2 ⁢ π | τ ) = M ⁢ θ 3 ⁡ ( z + 1 2 ⁢ π ⁢ τ | τ ) = M ⁢ θ 4 ⁡ ( z + 1 2 ⁢ π + 1 2 ⁢ π ⁢ τ | τ ) , Jacobi-theta-tau 2 𝑧 𝜏 Jacobi-theta-tau 1 𝑧 1 2 𝜋 𝜏 𝑀 Jacobi-theta-tau 3 𝑧 1 2 𝜋 𝜏 𝜏 𝑀 Jacobi-theta-tau 4 𝑧 1 2 𝜋 1 2 𝜋 𝜏 𝜏 {\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau\right)=\theta_{1}% \left(z+\tfrac{1}{2}\pi\middle|\tau\right)=M\theta_{3}\left(z+\tfrac{1}{2}\pi% \tau\middle|\tau\right)=M\theta_{4}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau% \middle|\tau\right),}}
    0 references
    DLMF id
    DLMF:20.2.E12
    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.m1ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1ldec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1ldec
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    DLMF:20.2.E10
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C20.S2.XMD1.m1bdec
    0 references
     
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