DLMF:19.2#Ex8 (Q6096)

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DLMF:19.2#Ex8
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    Defining formula
    F ⁡ ( m ⁢ π ± ϕ , k ) = 2 ⁢ m ⁢ K ⁡ ( k ) ± F ⁡ ( ϕ , k ) , elliptic-integral-first-kind-F plus-or-minus 𝑚 𝜋 italic-ϕ 𝑘 plus-or-minus 2 𝑚 complete-elliptic-integral-first-kind-K 𝑘 elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(m\pi\pm\phi,k\right)=2mK\left(k\right)\pm F% \left(\phi,k\right),}}
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    DLMF id
    DLMF:19.2#Ex8
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