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DLMF:29.3#Ex13

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Formula:9305
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MaRDI QIDQ9305

  • Label: DLMF:29.3#Ex13


Digital Library of Mathematical Functions ID 29.3#Ex13

∫ 0 K ⁡ dn ⁡ ( x , k ) ⁢ ( 𝐸𝑠 ν 2 ⁢ m + 2 ⁡ ( x , k 2 ) ) 2 ⁢ d x = 1 4 ⁢ π . superscript subscript 0 complete-elliptic-integral-first-kind-K 𝑘 Jacobi-elliptic-dn 𝑥 𝑘 superscript Lame-Es 2 𝑚 2 𝜈 𝑥 superscript 𝑘 2 2 𝑥 1 4 𝜋 {\displaystyle{\displaystyle\int_{0}^{K}\operatorname{dn}\left(x,k\right)\left% (\mathit{Es}^{2m+2}_{\nu}\left(x,k^{2}\right)\right)^{2}\mathrm{d}x=\frac{1}{4% }\pi.}}


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