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:15.10.E13 - MaRDI portal
Statements
w
3
(
z
)
=
F
(
a
,
b
a
+
b
-
c
+
1
;
1
-
z
)
=
z
1
-
c
F
(
a
-
c
+
1
,
b
-
c
+
1
a
+
b
-
c
+
1
;
1
-
z
)
=
z
-
a
F
(
a
,
a
-
c
+
1
a
+
b
-
c
+
1
;
1
-
1
z
)
=
z
-
b
F
(
b
,
b
-
c
+
1
a
+
b
-
c
+
1
;
1
-
1
z
)
.
subscript
𝑤
3
𝑧
Gauss-hypergeometric-F
𝑎
𝑏
𝑎
𝑏
𝑐
1
1
𝑧
superscript
𝑧
1
𝑐
Gauss-hypergeometric-F
𝑎
𝑐
1
𝑏
𝑐
1
𝑎
𝑏
𝑐
1
1
𝑧
superscript
𝑧
𝑎
Gauss-hypergeometric-F
𝑎
𝑎
𝑐
1
𝑎
𝑏
𝑐
1
1
1
𝑧
superscript
𝑧
𝑏
Gauss-hypergeometric-F
𝑏
𝑏
𝑐
1
𝑎
𝑏
𝑐
1
1
1
𝑧
{\displaystyle{\displaystyle w_{3}(z)=F\left({a,b\atop a+b-c+1};1-z\right)=z^{%
1-c}F\left({a-c+1,b-c+1\atop a+b-c+1};1-z\right)=z^{-a}F\left({a,a-c+1\atop a+%
b-c+1};1-\frac{1}{z}\right)=z^{-b}F\left({b,b-c+1\atop a+b-c+1};1-\frac{1}{z}%
\right).}}
F
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
w
m
(
z
)
subscript
𝑤
𝑚
𝑧
{\displaystyle{\displaystyle w_{m}(z)}}
Identifiers
