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:22.6.E22 - MaRDI portal
Statements
p
q
2
(
1
2
z
,
k
)
=
p
s
(
z
,
k
)
+
r
s
(
z
,
k
)
q
s
(
z
,
k
)
+
r
s
(
z
,
k
)
=
p
q
(
z
,
k
)
+
r
q
(
z
,
k
)
1
+
r
q
(
z
,
k
)
=
p
r
(
z
,
k
)
+
1
q
r
(
z
,
k
)
+
1
.
abstract-Jacobi-elliptic
p
q
2
1
2
𝑧
𝑘
abstract-Jacobi-elliptic
p
s
𝑧
𝑘
abstract-Jacobi-elliptic
r
s
𝑧
𝑘
abstract-Jacobi-elliptic
q
s
𝑧
𝑘
abstract-Jacobi-elliptic
r
s
𝑧
𝑘
abstract-Jacobi-elliptic
p
q
𝑧
𝑘
abstract-Jacobi-elliptic
r
q
𝑧
𝑘
1
abstract-Jacobi-elliptic
r
q
𝑧
𝑘
abstract-Jacobi-elliptic
p
r
𝑧
𝑘
1
abstract-Jacobi-elliptic
q
r
𝑧
𝑘
1
{\displaystyle{\displaystyle{\operatorname{pq}^{2}}\left(\tfrac{1}{2}z,k\right%
)=\frac{\operatorname{ps}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}{%
\operatorname{qs}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}=\frac{%
\operatorname{pq}\left(z,k\right)+\operatorname{rq}\left(z,k\right)}{1+%
\operatorname{rq}\left(z,k\right)}=\frac{\operatorname{pr}\left(z,k\right)+1}{%
\operatorname{qr}\left(z,k\right)+1}.}}
p
q
(
z
,
k
)
abstract-Jacobi-elliptic
p
q
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{pq}\left(\NVar{z},\NVar{k}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
