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DLMF:23.15.E7 - MaRDI portal

DLMF:23.15.E7 (Q8030)

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DLMF:23.15.E7
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    Statements

    DLMF defining formula
    J ⁡ ( τ ) = ( θ 2 8 ⁡ ( 0 , q ) + θ 3 8 ⁡ ( 0 , q ) + θ 4 8 ⁡ ( 0 , q ) ) 3 54 ⁢ ( θ 1 ′ ⁡ ( 0 , q ) ) 8 , Kleins-invariant-modular-J 𝜏 superscript Jacobi-theta 2 8 0 𝑞 Jacobi-theta 3 8 0 𝑞 Jacobi-theta 4 8 0 𝑞 3 54 superscript diffop Jacobi-theta 1 1 0 𝑞 8 {\displaystyle{\displaystyle J\left(\tau\right)=\frac{\left({\theta_{2}^{8}}% \left(0,q\right)+{\theta_{3}^{8}}\left(0,q\right)+{\theta_{4}^{8}}\left(0,q% \right)\right)^{3}}{54\left(\theta_{1}'\left(0,q\right)\right)^{8}},}}
    0 references
    Symbols used
    Q11948
    DLMF 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
    0 references
    nome
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1cdec
    0 references
    complex variable
    DLMF defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C23.S1.XMD9.m1cdec
    0 references

    Identifiers

     
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