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DLMF:19.7#Ex8 - MaRDI portal

DLMF:19.7#Ex8 (Q6885)

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DLMF:19.7#Ex8
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    DLMF defining formula
    E ⁡ ( 1 / k ′ ) = ( 1 / k ′ ) ⁢ ( E ⁡ ( k ′ ) ∓ i ⁢ E ⁡ ( k ) - k 2 ⁢ K ⁡ ( k ′ ) ± i ⁢ k ′ 2 ⁢ K ⁡ ( k ) ) , complete-elliptic-integral-second-kind-E 1 superscript 𝑘 ′ 1 superscript 𝑘 ′ plus-or-minus minus-or-plus complete-elliptic-integral-second-kind-E superscript 𝑘 ′ imaginary-unit complete-elliptic-integral-second-kind-E 𝑘 superscript 𝑘 2 complete-elliptic-integral-first-kind-K superscript 𝑘 ′ imaginary-unit superscript superscript 𝑘 ′ 2 complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle E\left(1/k^{\prime}\right)=(1/k^{\prime})\left(E% \left(k^{\prime}\right)\mp\mathrm{i}E\left(k\right)-k^{2}K\left(k^{\prime}% \right)\pm\mathrm{i}{k^{\prime}}^{2}K\left(k\right)\right),}}
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