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DLMF:29.3#Ex12 - MaRDI portal

DLMF:29.3#Ex12 (Q9304)

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DLMF:29.3#Ex12
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    DLMF defining formula
    ∫ 0 K ⁑ dn ⁑ ( x , k ) ⁒ ( 𝐸𝑠 Ξ½ 2 ⁒ m + 1 ⁑ ( x , k 2 ) ) 2 ⁒ d x = 1 4 ⁒ Ο€ , superscript subscript 0 complete-elliptic-integral-first-kind-K π‘˜ Jacobi-elliptic-dn π‘₯ π‘˜ superscript Lame-Es 2 π‘š 1 𝜈 π‘₯ superscript π‘˜ 2 2 π‘₯ 1 4 πœ‹ {\displaystyle{\displaystyle\int_{0}^{K}\operatorname{dn}\left(x,k\right)\left% (\mathit{Es}^{2m+1}_{\nu}\left(x,k^{2}\right)\right)^{2}\mathrm{d}x=\frac{1}{4% }\pi,}}
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