DLMF:19.33.E2 (Q6699)

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DLMF:19.33.E2
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    S 2 π = c 2 + a b sin ϕ ( E ( ϕ , k ) sin 2 ϕ + F ( ϕ , k ) cos 2 ϕ ) , 𝑆 2 𝜋 superscript 𝑐 2 𝑎 𝑏 italic-ϕ elliptic-integral-second-kind-E italic-ϕ 𝑘 2 italic-ϕ elliptic-integral-first-kind-F italic-ϕ 𝑘 2 italic-ϕ {\displaystyle{\displaystyle\frac{S}{2\pi}=c^{2}+\frac{ab}{\sin\phi}\left(E% \left(\phi,k\right){\sin^{2}}\phi+F\left(\phi,k\right){\cos^{2}}\phi\right),}}
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    a b c 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle a\geq b\geq c}}
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