DLMF:19.9.E16 (Q6259)

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DLMF:19.9.E16
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    F ( ϕ , k ) = 2 π K ( k ) ln ( 4 Δ + cos ϕ ) - θ Δ 2 , elliptic-integral-first-kind-F italic-ϕ 𝑘 2 𝜋 complete-elliptic-integral-first-kind-K superscript 𝑘 4 Δ italic-ϕ 𝜃 superscript Δ 2 {\displaystyle{\displaystyle F\left(\phi,k\right)=\frac{2}{\pi}K\left(k^{% \prime}\right)\ln\left(\frac{4}{\Delta+\cos\phi}\right)-\theta\Delta^{2},}}
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    DLMF:19.9.E16
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    ( sin ϕ ) / 8 < θ < ( ln 2 ) / ( k 2 sin ϕ ) italic-ϕ 8 𝜃 2 superscript 𝑘 2 italic-ϕ {\displaystyle{\displaystyle(\sin\phi)/8<\theta<(\ln 2)/(k^{2}\sin\phi)}}
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