DLMF:19.7#Ex10 (Q6191)

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DLMF:19.7#Ex10
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    Defining formula
    E ⁡ ( ϕ , k 1 ) = ( E ⁡ ( β , k ) - k ′ 2 ⁢ F ⁡ ( β , k ) ) / k , elliptic-integral-second-kind-E italic-ϕ subscript 𝑘 1 elliptic-integral-second-kind-E 𝛽 𝑘 superscript superscript 𝑘 ′ 2 elliptic-integral-first-kind-F 𝛽 𝑘 𝑘 {\displaystyle{\displaystyle E\left(\phi,k_{1}\right)=(E\left(\beta,k\right)-{% k^{\prime}}^{2}F\left(\beta,k\right))/k,}}
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    DLMF id
    DLMF:19.7#Ex10
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