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1
Wikipedia:Translation/*/How-to
2
Hankel function
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User
:
Takarazuka Family Land/memo
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From Wikipedia, the free encyclopedia
<
User:Takarazuka Family Land
Wikipedia:Translation/*/How-to
[
edit
]
Wikipedia:Translation/*/How-to
Hankel function
[
edit
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[1]
[2]
[3]
H
ϵ
[
z
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=
∫
C
ϵ
[
−
w
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z
−
1
e
−
w
1
−
e
−
w
d
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{\displaystyle H\epsilon [z]=\int _{C\epsilon }{\frac {[-w]^{z-1}e^{-w}}{1-e^{-w}}}dw}
For
I
[
w
]
<
0
,
|
a
r
g
(
−
w
)
|
<
π
,
ϵ
≠
2
π
k
>
0
W
h
e
r
e
C
ϵ
{\displaystyle I[w]<0,|arg(-w)|<\pi ,\epsilon \neq 2\pi k>0Where{C\epsilon }}
is
Hankel contour
![[2]](http://mathworld.wolfram.com/images/equations/HankelFunction/equation1.gif){kind=link}
![[3]](http://mathworld.wolfram.com/images/equations/HankelFunction/inline1.gif){kind=link}
![{\displaystyle H\epsilon [z]=\int _{C\epsilon }{\frac {[-w]^{z-1}e^{-w}}{1-e^{-w}}}dw}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eeacdeaa8633cc445c3c9db67c65a1a99f5f750c)
![{\displaystyle I[w]<0,|arg(-w)|<\pi ,\epsilon \neq 2\pi k>0Where{C\epsilon }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2286b54e87e8719a0d89e0fb3f24e947904d93a9)
is Hankel contour