DLMF:20.11.E8 (Q6849)

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DLMF:20.11.E8
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    Statements

    Defining formula
    φ m , n ⁡ ( z , q ) = θ n ⁡ ( 0 , q ) ⁢ θ m ⁡ ( z , q ) θ m ⁡ ( 0 , q ) ⁢ θ n ⁡ ( z , q ) , Jacobi-theta-combined 𝑚 𝑛 𝑧 𝑞 Jacobi-theta 𝑛 0 𝑞 Jacobi-theta 𝑚 𝑧 𝑞 Jacobi-theta 𝑚 0 𝑞 Jacobi-theta 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{m,n}\left(z,q\right)=\frac{\theta_{n}% \left(0,q\right)\theta_{m}\left(z,q\right)}{\theta_{m}\left(0,q\right)\theta_{% n}\left(z,q\right)},}}
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    DLMF id
    DLMF:20.11.E8
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    constraint
    m , n = 2 , 3 , 4 formulae-sequence 𝑚 𝑛 2 3 4 {\displaystyle{\displaystyle m,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.m2abdec
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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.m5abdec
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