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Statements
∫
0
K
(
k
)
ln
(
cn
(
t
,
k
)
)
d
t
=
-
1
4
K
′
(
k
)
+
1
2
K
(
k
)
ln
(
k
′
/
k
)
,
superscript
subscript
0
complete-elliptic-integral-first-kind-K
𝑘
Jacobi-elliptic-cn
𝑡
𝑘
𝑡
1
4
complementary-complete-elliptic-integral-first-kind-K
𝑘
1
2
complete-elliptic-integral-first-kind-K
𝑘
superscript
𝑘
′
𝑘
{\displaystyle{\displaystyle\int_{0}^{K\left(k\right)}\ln\left(\operatorname{%
cn}\left(t,k\right)\right)\mathrm{d}t=-\tfrac{1}{4}{K^{\prime}}\left(k\right)+%
\tfrac{1}{2}K\left(k\right)\ln\left(k^{\prime}/k\right),}}
cn
(
z
,
k
)
Jacobi-elliptic-cn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
K
′
(
k
)
complementary-complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
Identifiers
