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Statements
H
ν
(
1
)
(
z
)
∼
-
H
ν
(
2
)
(
z
)
∼
-
(
i
/
π
)
Γ
(
ν
)
(
1
2
z
)
-
ν
,
asymptotically-equals
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
asymptotically-equals
𝑖
𝜋
Euler-Gamma
𝜈
superscript
1
2
𝑧
𝜈
{\displaystyle{\displaystyle{H^{(1)}_{\nu}}\left(z\right)\sim-{H^{(2)}_{\nu}}%
\left(z\right)\sim-(i/\pi)\Gamma\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},}}
ℜ
ν
>
0
𝜈
0
{\displaystyle{\displaystyle\Re\nu>0}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\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)}}
∼
asymptotically-equals
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
