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DLMF:19.25#Ex5 - MaRDI portal

DLMF:19.25#Ex5 (Q7201)

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DLMF:19.25#Ex5
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    DLMF defining formula
    E ⁡ ( k ) - k ′ 2 ⁢ K ⁡ ( k ) = 1 3 ⁢ k 2 ⁢ k ′ 2 ⁢ R D ⁡ ( 0 , 1 , k ′ 2 ) . complete-elliptic-integral-second-kind-E 𝑘 superscript superscript 𝑘 ′ 2 complete-elliptic-integral-first-kind-K 𝑘 1 3 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Carlson-integral-RD 0 1 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle E\left(k\right)-{k^{\prime}}^{2}K\left(k\right)=% \tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(0,1,{k^{\prime}}^{2}\right).}}
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