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Statements
H
ν
(
2
)
(
z
)
=
e
1
2
ν
π
i
2
π
2
∫
c
-
i
∞
c
+
i
∞
Γ
(
t
)
Γ
(
t
-
ν
)
(
1
2
i
z
)
ν
-
2
t
d
t
,
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
superscript
𝑒
1
2
𝜈
𝜋
𝑖
2
superscript
𝜋
2
superscript
subscript
𝑐
𝑖
𝑐
𝑖
Euler-Gamma
𝑡
Euler-Gamma
𝑡
𝜈
superscript
1
2
𝑖
𝑧
𝜈
2
𝑡
𝑡
{\displaystyle{\displaystyle{H^{(2)}_{\nu}}\left(z\right)=\frac{e^{\frac{1}{2}%
\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\Gamma\left(t\right)\Gamma%
\left(t-\nu\right)(\tfrac{1}{2}iz)^{\nu-2t}\mathrm{d}t,}}
-
π
<
ph
z
<
0
𝜋
phase
𝑧
0
{\displaystyle{\displaystyle-\pi<\operatorname{ph}z<0}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
H
ν
(
2
)
(
z
)
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
c
𝑐
{\displaystyle{\displaystyle c}}
