DLMF:22.2.E8 (Q6930)

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DLMF:22.2.E8
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    test
    cd ⁡ ( z , k ) = θ 3 ⁡ ( 0 , q ) θ 2 ⁡ ( 0 , q ) ⁢ θ 2 ⁡ ( ζ , q ) θ 3 ⁡ ( ζ , q ) = 1 dc ⁡ ( z , k ) , Jacobi-elliptic-cd 𝑧 𝑘 Jacobi-theta 3 0 𝑞 Jacobi-theta 2 0 𝑞 Jacobi-theta 2 𝜁 𝑞 Jacobi-theta 3 𝜁 𝑞 1 Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(z,k\right)=\frac{\theta_{3}% \left(0,q\right)}{\theta_{2}\left(0,q\right)}\frac{\theta_{2}\left(\zeta,q% \right)}{\theta_{3}\left(\zeta,q\right)}=\frac{1}{\operatorname{dc}\left(z,k% \right)},}}
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    DLMF:22.2.E8
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