DLMF:19.25.E10 (Q6514)

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DLMF:19.25.E10
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    test
    E ⁡ ( ϕ , k ) = k ′ 2 ⁢ R F ⁡ ( c - 1 , c - k 2 , c ) + 1 3 ⁢ k 2 ⁢ k ′ 2 ⁢ R D ⁡ ( c - 1 , c , c - k 2 ) + k 2 ⁢ ( c - 1 ) / ( c ⁢ ( c - k 2 ) ) , elliptic-integral-second-kind-E italic-ϕ 𝑘 superscript superscript 𝑘 ′ 2 Carlson-integral-RF 𝑐 1 𝑐 superscript 𝑘 2 𝑐 1 3 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Carlson-integral-RD 𝑐 1 𝑐 𝑐 superscript 𝑘 2 superscript 𝑘 2 𝑐 1 𝑐 𝑐 superscript 𝑘 2 {\displaystyle{\displaystyle E\left(\phi,k\right)={k^{\prime}}^{2}R_{F}\left(c% -1,c-k^{2},c\right)+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(c-1,c,c-k^{2}% \right)+k^{2}\sqrt{(c-1)/(c(c-k^{2}))},}}
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    DLMF id
    DLMF:19.25.E10
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