DLMF:22.2.E7 (Q6929)

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DLMF:22.2.E7
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    Statements

    Defining formula
    sd ⁡ ( z , k ) = θ 3 2 ⁡ ( 0 , q ) θ 2 ⁡ ( 0 , q ) ⁢ θ 4 ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( ζ , q ) θ 3 ⁡ ( ζ , q ) = 1 ds ⁡ ( z , k ) , Jacobi-elliptic-sd 𝑧 𝑘 Jacobi-theta 3 2 0 𝑞 Jacobi-theta 2 0 𝑞 Jacobi-theta 4 0 𝑞 Jacobi-theta 1 𝜁 𝑞 Jacobi-theta 3 𝜁 𝑞 1 Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(z,k\right)=\frac{{\theta_{3% }^{2}}\left(0,q\right)}{\theta_{2}\left(0,q\right)\theta_{4}\left(0,q\right)}% \frac{\theta_{1}\left(\zeta,q\right)}{\theta_{3}\left(\zeta,q\right)}=\frac{1}% {\operatorname{ds}\left(z,k\right)},}}
    0 references
    DLMF id
    DLMF:22.2.E7
    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.m2addec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2aedec
    0 references
     
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