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:22.11.E12 - MaRDI portal
Statements
sc
(
z
,
k
)
-
π
2
K
k
′
tan
ζ
=
2
π
K
k
′
∑
n
=
1
∞
(
-
1
)
n
q
2
n
sin
(
2
n
ζ
)
1
+
q
2
n
.
Jacobi-elliptic-sc
𝑧
𝑘
𝜋
2
𝐾
superscript
𝑘
′
𝜁
2
𝜋
𝐾
superscript
𝑘
′
superscript
subscript
𝑛
1
superscript
1
𝑛
superscript
𝑞
2
𝑛
2
𝑛
𝜁
1
superscript
𝑞
2
𝑛
{\displaystyle{\displaystyle\operatorname{sc}\left(z,k\right)-\frac{\pi}{2Kk^{%
\prime}}\tan\zeta=\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{%
2n}\sin\left(2n\zeta\right)}{1+q^{2n}}.}}
sc
(
z
,
k
)
Jacobi-elliptic-sc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sc}\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)}}
q
𝑞
{\displaystyle{\displaystyle q}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
