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:5.17.E5 - MaRDI portal
Statements
Ln
G
(
z
+
1
)
∼
1
4
z
2
+
z
Ln
Γ
(
z
+
1
)
-
(
1
2
z
(
z
+
1
)
+
1
12
)
Ln
z
-
ln
A
+
∑
k
=
1
∞
B
2
k
+
2
2
k
(
2
k
+
1
)
(
2
k
+
2
)
z
2
k
.
asymptotic-expansion
multivalued-natural-logarithm
Barnes-Gamma
𝑧
1
1
4
superscript
𝑧
2
𝑧
multivalued-natural-logarithm
Euler-Gamma
𝑧
1
1
2
𝑧
𝑧
1
1
12
multivalued-natural-logarithm
𝑧
𝐴
superscript
subscript
𝑘
1
Bernoulli-number-B
2
𝑘
2
2
𝑘
2
𝑘
1
2
𝑘
2
superscript
𝑧
2
𝑘
{\displaystyle{\displaystyle\operatorname{Ln}G\left(z+1\right)\sim\tfrac{1}{4}%
z^{2}+z\operatorname{Ln}\Gamma\left(z+1\right)-\left(\tfrac{1}{2}z(z+1)+\tfrac%
{1}{12}\right)\operatorname{Ln}z-\ln A+\sum_{k=1}^{\infty}\frac{B_{2k+2}}{2k(2%
k+1)(2k+2)z^{2k}}.}}
G
(
z
)
Barnes-Gamma
𝑧
{\displaystyle{\displaystyle G\left(\NVar{z}\right)}}
B
n
Bernoulli-number-B
𝑛
{\displaystyle{\displaystyle B_{\NVar{n}}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
Ln
z
multivalued-natural-logarithm
𝑧
{\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
A
𝐴
{\displaystyle{\displaystyle A}}
Identifiers
