DLMF:23.5#Ex8 (Q7234)

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DLMF:23.5#Ex8
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    Defining formula
    K ⁡ ( k ) = K ′ ⁡ ( k ) = ( Γ ⁡ ( 1 4 ) ) 2 / ( 4 ⁢ π ) . complete-elliptic-integral-first-kind-K 𝑘 diffop complete-elliptic-integral-first-kind-K 1 𝑘 superscript Euler-Gamma 1 4 2 4 𝜋 {\displaystyle{\displaystyle K\left(k\right)=K'\left(k\right)=\ifrac{\left(% \Gamma\left(\tfrac{1}{4}\right)\right)^{2}}{\left(4\sqrt{\pi}\right)}.}}
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    DLMF id
    DLMF:23.5#Ex8
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