DLMF:20.11.E6 (Q6847)

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DLMF:20.11.E6
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    Statements

    Defining formula
    φ m , 1 ⁡ ( z , q ) = θ 1 ′ ⁡ ( 0 , q ) ⁢ θ m ⁡ ( z , q ) θ m ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( z , q ) , Jacobi-theta-combined 𝑚 1 𝑧 𝑞 diffop Jacobi-theta 1 1 0 𝑞 Jacobi-theta 𝑚 𝑧 𝑞 Jacobi-theta 𝑚 0 𝑞 Jacobi-theta 1 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{m,1}\left(z,q\right)=\frac{\theta_{1}'% \left(0,q\right)\theta_{m}\left(z,q\right)}{\theta_{m}\left(0,q\right)\theta_{% 1}\left(z,q\right)},}}
    0 references
    DLMF id
    DLMF:20.11.E6
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    constraint
    m = 2 , 3 , 4 𝑚 2 3 4 {\displaystyle{\displaystyle m=2,3,4}}
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    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.m2adec
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    Q11955
    Defining formula
    φ n , m ⁡ ( z , q ) Jacobi-theta-combined 𝑛 𝑚 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{\NVar{n},\NVar{m}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C20.S11.SS5.p2.m5adec
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    Q11951
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C20.S1.XMD1.m1bdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1adec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1dec
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