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 2.5.E10 - MaRDI portal
Statements
ℳ
h
(
z
)
=
2
z
-
1
Γ
(
ν
+
1
2
z
)
Γ
2
(
1
-
1
2
z
)
Γ
(
1
+
ν
-
1
2
z
)
Γ
(
z
)
π
sin
(
π
z
)
,
Mellin-transform
ℎ
𝑧
superscript
2
𝑧
1
Euler-Gamma
𝜈
1
2
𝑧
Euler-Gamma
2
1
1
2
𝑧
Euler-Gamma
1
𝜈
1
2
𝑧
Euler-Gamma
𝑧
𝜋
𝜋
𝑧
{\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z%
\right)=\frac{2^{z-1}\Gamma\left(\nu+\frac{1}{2}z\right)}{{\Gamma^{2}}\left(1-%
\frac{1}{2}z\right)\Gamma\left(1+\nu-\frac{1}{2}z\right)\Gamma\left(z\right)}%
\frac{\pi}{\sin\left(\pi z\right)},}}
-
2
ν
<
ℜ
z
<
1
2
𝜈
𝑧
1
{\displaystyle{\displaystyle-2\nu<\Re z<1}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
ℳ
(
f
)
(
s
)
Mellin-transform
𝑓
𝑠
{\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
h
(
t
)
=
J
ν
2
(
t
)
ℎ
𝑡
Bessel-J
𝜈
2
𝑡
{\displaystyle{\displaystyle h(t)={J_{\nu}^{2}}\left(t\right)}}
f
(
t
)
=
1
/
(
1
+
t
)
𝑓
𝑡
1
1
𝑡
{\displaystyle{\displaystyle f(t)=1/(1+t)}}
