DLMF:20.7.E10 (Q6805)

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DLMF:20.7.E10
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    Statements

    Defining formula
    θ 1 ⁡ ( 2 ⁢ z , q ) = 2 ⁢ θ 1 ⁡ ( z , q ) ⁢ θ 2 ⁡ ( z , q ) ⁢ θ 3 ⁡ ( z , q ) ⁢ θ 4 ⁡ ( z , q ) θ 2 ⁡ ( 0 , q ) ⁢ θ 3 ⁡ ( 0 , q ) ⁢ θ 4 ⁡ ( 0 , q ) . Jacobi-theta 1 2 𝑧 𝑞 2 Jacobi-theta 1 𝑧 𝑞 Jacobi-theta 2 𝑧 𝑞 Jacobi-theta 3 𝑧 𝑞 Jacobi-theta 4 𝑧 𝑞 Jacobi-theta 2 0 𝑞 Jacobi-theta 3 0 𝑞 Jacobi-theta 4 0 𝑞 {\displaystyle{\displaystyle\theta_{1}\left(2z,q\right)=2\frac{\theta_{1}\left% (z,q\right)\theta_{2}\left(z,q\right)\theta_{3}\left(z,q\right)\theta_{4}\left% (z,q\right)}{\theta_{2}\left(0,q\right)\theta_{3}\left(0,q\right)\theta_{4}% \left(0,q\right)}.}}
    0 references
    DLMF id
    DLMF:20.7.E10
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2aidec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1hdec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1idec
    0 references
     
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