DLMF:22.6.E22 (Q6956)

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DLMF:22.6.E22
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    test
    p ⁣ q 2 ⁡ ( 1 2 ⁢ z , k ) = p ⁣ s ⁡ ( z , k ) + r ⁣ s ⁡ ( z , k ) q ⁣ s ⁡ ( z , k ) + r ⁣ s ⁡ ( z , k ) = p ⁣ q ⁡ ( z , k ) + r ⁣ q ⁡ ( z , k ) 1 + r ⁣ q ⁡ ( z , k ) = p ⁣ r ⁡ ( z , k ) + 1 q ⁣ r ⁡ ( z , k ) + 1 . abstract-Jacobi-elliptic p q 2 1 2 𝑧 𝑘 abstract-Jacobi-elliptic p s 𝑧 𝑘 abstract-Jacobi-elliptic r s 𝑧 𝑘 abstract-Jacobi-elliptic q s 𝑧 𝑘 abstract-Jacobi-elliptic r s 𝑧 𝑘 abstract-Jacobi-elliptic p q 𝑧 𝑘 abstract-Jacobi-elliptic r q 𝑧 𝑘 1 abstract-Jacobi-elliptic r q 𝑧 𝑘 abstract-Jacobi-elliptic p r 𝑧 𝑘 1 abstract-Jacobi-elliptic q r 𝑧 𝑘 1 {\displaystyle{\displaystyle{\operatorname{pq}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{\operatorname{ps}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}{% \operatorname{qs}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}=\frac{% \operatorname{pq}\left(z,k\right)+\operatorname{rq}\left(z,k\right)}{1+% \operatorname{rq}\left(z,k\right)}=\frac{\operatorname{pr}\left(z,k\right)+1}{% \operatorname{qr}\left(z,k\right)+1}.}}
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    DLMF id
    DLMF:22.6.E22
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