DLMF:19.25#Ex4 (Q6504)

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DLMF:19.25#Ex4
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    Defining formula
    K ⁡ ( k ) - E ⁡ ( k ) = k 2 ⁢ D ⁡ ( k ) = 1 3 ⁢ k 2 ⁢ R D ⁡ ( 0 , k ′ 2 , 1 ) , complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-second-kind-E 𝑘 superscript 𝑘 2 complete-elliptic-integral-D 𝑘 1 3 superscript 𝑘 2 Carlson-integral-RD 0 superscript superscript 𝑘 ′ 2 1 {\displaystyle{\displaystyle K\left(k\right)-E\left(k\right)=k^{2}D\left(k% \right)=\tfrac{1}{3}k^{2}R_{D}\left(0,{k^{\prime}}^{2},1\right),}}
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    DLMF id
    DLMF:19.25#Ex4
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