DLMF:19.7#Ex5 (Q6186)

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DLMF:19.7#Ex5
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    K ⁡ ( 1 / k ) = k ⁢ ( K ⁡ ( k ) ∓ i ⁢ K ⁡ ( k ′ ) ) , complete-elliptic-integral-first-kind-K 1 𝑘 𝑘 minus-or-plus complete-elliptic-integral-first-kind-K 𝑘 imaginary-unit complete-elliptic-integral-first-kind-K superscript 𝑘 ′ {\displaystyle{\displaystyle K\left(1/k\right)=k(K\left(k\right)\mp\mathrm{i}K% \left(k^{\prime}\right)),}}
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    DLMF:19.7#Ex5
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