DLMF:22.2.E6 (Q6928)

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DLMF:22.2.E6
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    test
    dn ⁡ ( z , k ) = θ 4 ⁡ ( 0 , q ) θ 3 ⁡ ( 0 , q ) ⁢ θ 3 ⁡ ( ζ , q ) θ 4 ⁡ ( ζ , q ) = 1 nd ⁡ ( z , k ) , Jacobi-elliptic-dn 𝑧 𝑘 Jacobi-theta 4 0 𝑞 Jacobi-theta 3 0 𝑞 Jacobi-theta 3 𝜁 𝑞 Jacobi-theta 4 𝜁 𝑞 1 Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=\frac{\theta_{4}% \left(0,q\right)}{\theta_{3}\left(0,q\right)}\frac{\theta_{3}\left(\zeta,q% \right)}{\theta_{4}\left(\zeta,q\right)}=\frac{1}{\operatorname{nd}\left(z,k% \right)},}}
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    DLMF:22.2.E6
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