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.E43 - MaRDI portal
Statements
ℒ
h
(
ζ
)
=
ℳ
h
1
(
1
)
+
∑
ℜ
β
0
≤
ℜ
z
≤
1
res
[
-
ζ
z
-
1
Γ
(
1
-
z
)
ℳ
h
2
(
z
)
]
+
∑
1
<
ℜ
z
<
l
res
[
-
ζ
z
-
1
Γ
(
1
-
z
)
ℳ
h
(
z
)
]
+
1
2
π
i
∫
l
-
δ
-
i
∞
l
-
δ
+
i
∞
ζ
z
-
1
Γ
(
1
-
z
)
ℳ
h
(
z
)
d
z
,
Laplace-transform
ℎ
𝜁
Mellin-transform
subscript
ℎ
1
1
subscript
subscript
𝛽
0
𝑧
1
residue
delimited-[]
superscript
𝜁
𝑧
1
Euler-Gamma
1
𝑧
Mellin-transform
subscript
ℎ
2
𝑧
subscript
1
𝑧
𝑙
residue
delimited-[]
superscript
𝜁
𝑧
1
Euler-Gamma
1
𝑧
Mellin-transform
ℎ
𝑧
1
2
𝜋
𝑖
superscript
subscript
𝑙
𝛿
𝑖
𝑙
𝛿
𝑖
superscript
𝜁
𝑧
1
Euler-Gamma
1
𝑧
Mellin-transform
ℎ
𝑧
𝑧
{\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta%
\right)=\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right)+\sum_{\Re%
\beta_{0}\leq\Re z\leq 1}\Residue\left[-\zeta^{z-1}\Gamma\left(1-z\right)%
\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]+\sum\limits_{1%
<\Re z<l}\Residue\left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0%
mu h\mskip 3.0mu \left(z\right)\right]+\frac{1}{2\pi i}\int_{l-\delta-i\infty}%
^{l-\delta+i\infty}\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h%
\mskip 3.0mu \left(z\right)\mathrm{d}z,}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
ℒ
(
f
)
(
s
)
Laplace-transform
𝑓
𝑠
{\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}%
\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}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
res
residue
{\displaystyle{\displaystyle\Residue}}
h
(
x
)
ℎ
𝑥
{\displaystyle{\displaystyle h(x)}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
Identifiers
