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:31.10.E11 - MaRDI portal
Statements
π¦
β’
(
z
,
t
)
=
(
z
β’
t
-
a
)
1
2
-
Ξ΄
-
Ο
β’
(
z
β’
t
/
a
)
-
1
2
+
Ξ΄
+
Ο
-
Ξ±
β’
F
1
2
β‘
(
1
2
-
Ξ΄
-
Ο
+
Ξ±
,
3
2
-
Ξ΄
-
Ο
+
Ξ±
-
Ξ³
Ξ±
-
Ξ²
+
1
;
a
z
β’
t
)
β’
P
β‘
{
0
1
β
0
0
-
1
2
+
Ξ΄
+
Ο
(
z
-
a
)
β’
(
t
-
a
)
(
1
-
a
)
β’
(
z
β’
t
-
a
)
1
-
Ο΅
1
-
Ξ΄
-
1
2
+
Ο΅
-
Ο
}
.
π¦
π§
π‘
superscript
π§
π‘
π
1
2
πΏ
π
superscript
π§
π‘
π
1
2
πΏ
π
πΌ
Gauss-hypergeometric-F-as-2F1
1
2
πΏ
π
πΌ
3
2
πΏ
π
πΌ
πΎ
πΌ
π½
1
π
π§
π‘
Riemann-P-symbol
0
1
absent
0
0
1
2
πΏ
π
π§
π
π‘
π
1
π
π§
π‘
π
1
italic-Ο΅
1
πΏ
1
2
italic-Ο΅
π
absent
{\displaystyle{\displaystyle\mathcal{K}(z,t)=(zt-a)^{\frac{1}{2}-\delta-\sigma%
}\left(\ifrac{zt}{a}\right)^{-\frac{1}{2}+\delta+\sigma-\alpha}\*{{}_{2}F_{1}}%
\left({\frac{1}{2}-\delta-\sigma+\alpha,\frac{3}{2}-\delta-\sigma+\alpha-%
\gamma\atop\alpha-\beta+1};\frac{a}{zt}\right)\*P\begin{Bmatrix}0&1&\infty&\\
0&0&-\frac{1}{2}+\delta+\sigma&\dfrac{(z-a)(t-a)}{(1-a)(zt-a)}\\
1-\epsilon&1-\delta&-\frac{1}{2}+\epsilon-\sigma&\end{Bmatrix}.}}
F
1
2
β‘
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F-as-2F1
π
π
π
π§
{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};%
\NVar{z}\right)}}
P
β‘
{
Ξ±
Ξ²
Ξ³
a
1
b
1
c
1
z
a
2
b
2
c
2
}
Riemann-P-symbol
πΌ
π½
πΎ
absent
subscript
π
1
subscript
π
1
subscript
π
1
π§
subscript
π
2
subscript
π
2
subscript
π
2
absent
{\displaystyle{\displaystyle P\NVar{\begin{Bmatrix}\alpha&\beta&\gamma&\\
a_{1}&b_{1}&c_{1}&z\\
a_{2}&b_{2}&c_{2}&\end{Bmatrix}}}}
z
π§
{\displaystyle{\displaystyle z}}
Ξ³
πΎ
{\displaystyle{\displaystyle\gamma}}
Ξ΄
πΏ
{\displaystyle{\displaystyle\delta}}
Ο΅
italic-Ο΅
{\displaystyle{\displaystyle\epsilon}}
a
π
{\displaystyle{\displaystyle a}}
Ξ±
πΌ
{\displaystyle{\displaystyle\alpha}}
Ξ²
π½
{\displaystyle{\displaystyle\beta}}
π¦
β’
(
z
,
t
)
π¦
π§
π‘
{\displaystyle{\displaystyle\mathcal{K}(z,t)}}
Ο
π
{\displaystyle{\displaystyle\sigma}}
