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.E40 - MaRDI portal
Statements
I
j
(
x
)
=
1
2
π
i
∫
p
j
-
i
∞
p
j
+
i
∞
x
-
z
Γ
(
1
-
z
)
ℳ
h
j
(
z
)
d
z
,
subscript
𝐼
𝑗
𝑥
1
2
𝜋
𝑖
superscript
subscript
subscript
𝑝
𝑗
𝑖
subscript
𝑝
𝑗
𝑖
superscript
𝑥
𝑧
Euler-Gamma
1
𝑧
Mellin-transform
subscript
ℎ
𝑗
𝑧
𝑧
{\displaystyle{\displaystyle I_{j}(x)=\frac{1}{2\pi i}\int_{p_{j}-i\infty}^{p_%
{j}+i\infty}x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{j}\mskip 3.%
0mu \left(z\right)\mathrm{d}z,}}
j
=
1
,
2
𝑗
1
2
{\displaystyle{\displaystyle j=1,2}}
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}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
h
(
x
)
ℎ
𝑥
{\displaystyle{\displaystyle h(x)}}
I
j
(
x
)
subscript
𝐼
𝑗
𝑥
{\displaystyle{\displaystyle I_{j}(x)}}
p
j
subscript
𝑝
𝑗
{\displaystyle{\displaystyle p_{j}}}
Identifiers
