Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:22.12.E13 - MaRDI portal
Statements
2
K
cs
(
2
K
t
,
k
)
=
lim
N
→
∞
∑
n
=
-
N
N
(
-
1
)
n
π
tan
(
π
(
t
-
n
τ
)
)
=
lim
N
→
∞
∑
n
=
-
N
N
(
-
1
)
n
(
lim
M
→
∞
∑
m
=
-
M
M
1
t
-
m
-
n
τ
)
.
2
𝐾
Jacobi-elliptic-cs
2
𝐾
𝑡
𝑘
subscript
→
𝑁
superscript
subscript
𝑛
𝑁
𝑁
superscript
1
𝑛
𝜋
𝜋
𝑡
𝑛
𝜏
subscript
→
𝑁
superscript
subscript
𝑛
𝑁
𝑁
superscript
1
𝑛
subscript
→
𝑀
superscript
subscript
𝑚
𝑀
𝑀
1
𝑡
𝑚
𝑛
𝜏
{\displaystyle{\displaystyle 2K\operatorname{cs}\left(2Kt,k\right)=\lim_{N\to%
\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan\left(\pi(t-n\tau)\right)}=\lim_{%
N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{%
1}{t-m-n\tau}\right).}}
cs
(
z
,
k
)
Jacobi-elliptic-cs
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
π
{\displaystyle{\displaystyle\pi}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
Identifiers
