DLMF:22.2.E7 (Q6929)

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DLMF:22.2.E7
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    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)},}}
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    DLMF:22.2.E7
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