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Statements
ber
ν
(
ν
x
)
+
i
bei
ν
(
ν
x
)
∼
e
ν
ξ
(
2
π
ν
ξ
)
1
/
2
(
x
e
3
π
i
/
4
1
+
ξ
)
ν
∑
k
=
0
∞
U
k
(
ξ
-
1
)
ν
k
,
asymptotic-expansion
Kelvin-ber
𝜈
𝜈
𝑥
𝑖
Kelvin-bei
𝜈
𝜈
𝑥
superscript
𝑒
𝜈
𝜉
superscript
2
𝜋
𝜈
𝜉
1
2
superscript
𝑥
superscript
𝑒
3
𝜋
𝑖
4
1
𝜉
𝜈
superscript
subscript
𝑘
0
subscript
𝑈
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}}{(2\pi\nu\xi)^{%
\ifrac{1}{2}}}\left(\frac{xe^{3\pi i/4}}{1+\xi}\right)^{\nu}\sum_{k=0}^{\infty%
}\frac{U_{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}}
U
k
(
p
)
subscript
𝑈
𝑘
𝑝
{\displaystyle{\displaystyle U_{k}(p)}}
ξ
𝜉
{\displaystyle{\displaystyle\xi}}
Identifiers
