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Statements
ker
ν
′
(
ν
x
)
+
i
kei
ν
′
(
ν
x
)
∼
-
e
-
ν
ξ
x
(
π
ξ
2
ν
)
1
/
2
(
x
e
3
π
i
/
4
1
+
ξ
)
-
ν
∑
k
=
0
∞
(
-
1
)
k
V
k
(
ξ
-
1
)
ν
k
,
asymptotic-expansion
diffop
Kelvin-ker
𝜈
1
𝜈
𝑥
𝑖
diffop
Kelvin-kei
𝜈
1
𝜈
𝑥
superscript
𝑒
𝜈
𝜉
𝑥
superscript
𝜋
𝜉
2
𝜈
1
2
superscript
𝑥
superscript
𝑒
3
𝜋
𝑖
4
1
𝜉
𝜈
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑉
𝑘
superscript
𝜉
1
superscript
𝜈
𝑘
{\displaystyle{\displaystyle\operatorname{ker}_{\nu}'\left(\nu x\right)+i%
\operatorname{kei}_{\nu}'\left(\nu x\right)\sim-\frac{e^{-\nu\xi}}{x}\left(%
\frac{\pi\xi}{2\nu}\right)^{\ifrac{1}{2}}\left(\frac{xe^{3\pi i/4}}{1+\xi}%
\right)^{-\nu}\*\sum_{k=0}^{\infty}(-1)^{k}\frac{V_{k}(\xi^{-1})}{\nu^{k}},}}
kei
ν
(
x
)
Kelvin-kei
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
ker
ν
(
x
)
Kelvin-ker
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{ker}_{\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
