DLMF:20.11.E7 (Q6848)

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DLMF:20.11.E7
No description defined

    Statements

    Defining formula
    φ 1 , n ⁡ ( z , q ) = θ n ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( z , q ) θ 1 ′ ⁡ ( 0 , q ) ⁢ θ n ⁡ ( z , q ) , Jacobi-theta-combined 1 𝑛 𝑧 𝑞 Jacobi-theta 𝑛 0 𝑞 Jacobi-theta 1 𝑧 𝑞 diffop Jacobi-theta 1 1 0 𝑞 Jacobi-theta 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{1,n}\left(z,q\right)=\frac{\theta_{n}% \left(0,q\right)\theta_{1}\left(z,q\right)}{\theta_{1}'\left(0,q\right)\theta_% {n}\left(z,q\right)},}}
    0 references
    DLMF id
    DLMF:20.11.E7
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    constraint
    n = 2 , 3 , 4 𝑛 2 3 4 {\displaystyle{\displaystyle n=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.m2aadec
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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.m5aadec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1cdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1bdec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1adec
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