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.E3 - MaRDI portal
Statements
F
0
′
(
η
,
ρ
)
G
0
′
(
η
,
ρ
)
∼
-
π
1
/
2
(
2
η
)
-
1
/
6
{
Ai
(
x
)
Bi
(
x
)
(
B
1
′
+
x
A
1
μ
+
B
2
′
+
x
A
2
μ
2
+
⋯
)
+
Ai
′
(
x
)
Bi
′
(
x
)
(
B
1
+
A
1
′
μ
+
B
2
+
A
2
′
μ
2
+
⋯
)
}
,
asymptotic-expansion
FRACOP
diffop
regular-Coulomb-F
0
1
𝜂
𝜌
diffop
irregular-Coulomb-G
0
1
𝜂
𝜌
superscript
𝜋
1
2
superscript
2
𝜂
1
6
FRACOP
Airy-Ai
𝑥
Airy-Bi
𝑥
superscript
subscript
𝐵
1
′
𝑥
subscript
𝐴
1
𝜇
superscript
subscript
𝐵
2
′
𝑥
subscript
𝐴
2
superscript
𝜇
2
⋯
FRACOP
diffop
Airy-Ai
1
𝑥
diffop
Airy-Bi
1
𝑥
subscript
𝐵
1
superscript
subscript
𝐴
1
′
𝜇
subscript
𝐵
2
superscript
subscript
𝐴
2
′
superscript
𝜇
2
⋯
{\displaystyle{\displaystyle{F_{0}'\left(\eta,\rho\right)\atop G_{0}'\left(%
\eta,\rho\right)}\sim-\pi^{1/2}(2\eta)^{-1/6}\left\{{\mathrm{Ai}\left(x\right)%
\atop\mathrm{Bi}\left(x\right)}\left(\frac{B_{1}^{\prime}+xA_{1}}{\mu}+\frac{B%
_{2}^{\prime}+xA_{2}}{\mu^{2}}+\cdots\right)+{\mathrm{Ai}'\left(x\right)\atop%
\mathrm{Bi}'\left(x\right)}\left(\frac{B_{1}+A_{1}^{\prime}}{\mu}+\frac{B_{2}+%
A_{2}^{\prime}}{\mu^{2}}+\cdots\right)\right\},}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
Bi
(
z
)
Airy-Bi
𝑧
{\displaystyle{\displaystyle\mathrm{Bi}\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)}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
A
j
subscript
𝐴
𝑗
{\displaystyle{\displaystyle A_{j}}}
B
j
subscript
𝐵
𝑗
{\displaystyle{\displaystyle B_{j}}}
Identifiers
