DLMF:20.7.E21 (Q6816)

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DLMF:20.7.E21
No description defined

    Statements

    Defining formula
    θ 1 ⁡ ( 4 ⁢ z | 4 ⁢ τ ) = B ⁢ θ 1 ⁡ ( z | τ ) ⁢ θ 1 ⁡ ( 1 4 ⁢ π - z | τ ) ⁢ θ 1 ⁡ ( 1 4 ⁢ π + z | τ ) ⁢ θ 2 ⁡ ( z | τ ) , Jacobi-theta-tau 1 4 𝑧 4 𝜏 𝐵 Jacobi-theta-tau 1 𝑧 𝜏 Jacobi-theta-tau 1 1 4 𝜋 𝑧 𝜏 Jacobi-theta-tau 1 1 4 𝜋 𝑧 𝜏 Jacobi-theta-tau 2 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{1}\left(4z\middle|4\tau\right)=B\theta_{1}% \left(z\middle|\tau\right)\theta_{1}\left(\tfrac{1}{4}\pi-z\middle|\tau\right)% \*\theta_{1}\left(\tfrac{1}{4}\pi+z\middle|\tau\right)\theta_{2}\left(z\middle% |\tau\right),}}
    0 references
    DLMF id
    DLMF:20.7.E21
    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.m1afdec
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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.m2acdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1qdec
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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1fdec
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    DLMF:20.7.E20
    Defining formula
    B 𝐵 {\displaystyle{\displaystyle B}}
    xml-id
    C20.S7.XMD2.m1adec
    0 references
     
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