DLMF:19.25.E9 (Q6513)

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DLMF:19.25.E9
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    E ( ϕ , k ) = R F ( c - 1 , c - k 2 , c ) - 1 3 k 2 R D ( c - 1 , c - k 2 , c ) , elliptic-integral-second-kind-E italic-ϕ 𝑘 Carlson-integral-RF 𝑐 1 𝑐 superscript 𝑘 2 𝑐 1 3 superscript 𝑘 2 Carlson-integral-RD 𝑐 1 𝑐 superscript 𝑘 2 𝑐 {\displaystyle{\displaystyle E\left(\phi,k\right)=R_{F}\left(c-1,c-k^{2},c% \right)-\tfrac{1}{3}k^{2}R_{D}\left(c-1,c-k^{2},c\right),}}
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