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DLMF:29.3#Ex13
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Formula:9305
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MaRDI QID
Q9305
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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