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:33.12.E7 - MaRDI portal
Statements
F
0
′
(
η
,
2
η
)
3
-
1
/
2
G
0
′
(
η
,
2
η
)
∼
Γ
(
2
3
)
2
π
ω
1
/
2
(
±
1
+
1
15
Γ
(
1
3
)
Γ
(
2
3
)
1
ω
2
±
2
14175
1
ω
6
+
1436
23 38875
Γ
(
1
3
)
Γ
(
2
3
)
1
ω
8
±
⋯
)
,
asymptotic-expansion
FRACOP
diffop
regular-Coulomb-F
0
1
𝜂
2
𝜂
superscript
3
1
2
diffop
irregular-Coulomb-G
0
1
𝜂
2
𝜂
Euler-Gamma
2
3
2
𝜋
superscript
𝜔
1
2
plus-or-minus
plus-or-minus
plus-or-minus
1
1
15
Euler-Gamma
1
3
Euler-Gamma
2
3
1
superscript
𝜔
2
2
14175
1
superscript
𝜔
6
1436
23 38875
Euler-Gamma
1
3
Euler-Gamma
2
3
1
superscript
𝜔
8
⋯
{\displaystyle{\displaystyle{F_{0}'\left(\eta,2\eta\right)\atop{3^{-\ifrac{1}{%
2}}G_{0}'\left(\eta,2\eta\right)}}\sim\frac{\Gamma\left(\frac{2}{3}\right)}{2%
\sqrt{\pi}\omega^{1/2}}\left(\pm 1+\frac{1}{15}\frac{\Gamma\left(\frac{1}{3}%
\right)}{\Gamma\left(\frac{2}{3}\right)}\frac{1}{\omega^{2}}\pm\frac{2}{14175}%
\frac{1}{\omega^{6}}+\frac{1436}{23\,38875}\frac{\Gamma\left(\frac{1}{3}\right%
)}{\Gamma\left(\frac{2}{3}\right)}\frac{1}{\omega^{8}}\pm\cdots\right),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
G
ℓ
(
η
,
ρ
)
irregular-Coulomb-G
ℓ
𝜂
𝜌
{\displaystyle{\displaystyle G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}%
\right)}}
F
ℓ
(
η
,
ρ
)
regular-Coulomb-F
ℓ
𝜂
𝜌
{\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}%
\right)}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
ω
𝜔
{\displaystyle{\displaystyle\omega}}
