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:10.69.E4 - MaRDI portal
Statements
ber
ν
′
(
ν
x
)
+
i
bei
ν
′
(
ν
x
)
∼
e
ν
ξ
x
(
ξ
2
π
ν
)
1
/
2
(
x
e
3
π
i
/
4
1
+
ξ
)
ν
∑
k
=
0
∞
V
k
(
ξ
-
1
)
ν
k
,
asymptotic-expansion
diffop
Kelvin-ber
𝜈
1
𝜈
𝑥
𝑖
diffop
Kelvin-bei
𝜈
1
𝜈
𝑥
superscript
𝑒
𝜈
𝜉
𝑥
superscript
𝜉
2
𝜋
𝜈
1
2
superscript
𝑥
superscript
𝑒
3
𝜋
𝑖
4
1
𝜉
𝜈
superscript
subscript
𝑘
0
subscript
𝑉
𝑘
superscript
𝜉
1
superscript
𝜈
𝑘
{\displaystyle{\displaystyle\operatorname{ber}_{\nu}'\left(\nu x\right)+i%
\operatorname{bei}_{\nu}'\left(\nu x\right)\sim\frac{e^{\nu\xi}}{x}\left(\frac%
{\xi}{2\pi\nu}\right)^{\ifrac{1}{2}}\left(\frac{xe^{3\pi i/4}}{1+\xi}\right)^{%
\nu}\sum_{k=0}^{\infty}\frac{V_{k}(\xi^{-1})}{\nu^{k}},}}
bei
ν
(
x
)
Kelvin-bei
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
ber
ν
(
x
)
Kelvin-ber
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
k
𝑘
{\displaystyle{\displaystyle k}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
V
k
(
p
)
subscript
𝑉
𝑘
𝑝
{\displaystyle{\displaystyle V_{k}(p)}}
ξ
𝜉
{\displaystyle{\displaystyle\xi}}
Identifiers
