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Statements
H
ν
(
1
)
(
z
)
H
ν
(
2
)
(
z
)
}
=
∓
2
π
-
1
2
i
e
∓
ν
π
i
(
2
z
)
ν
e
±
i
z
U
(
ν
+
1
2
,
2
ν
+
1
,
∓
2
i
z
)
.
selection
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
minus-or-plus
2
superscript
𝜋
1
2
𝑖
superscript
𝑒
minus-or-plus
𝜈
𝜋
𝑖
superscript
2
𝑧
𝜈
superscript
𝑒
plus-or-minus
𝑖
𝑧
Kummer-confluent-hypergeometric-U
𝜈
1
2
2
𝜈
1
minus-or-plus
2
𝑖
𝑧
{\displaystyle{\displaystyle\rselection{{H^{(1)}_{\nu}}\left(z\right)\\
{H^{(2)}_{\nu}}\left(z\right)}=\mp 2\pi^{-\frac{1}{2}}ie^{\mp\nu\pi i}(2z)^{%
\nu}\*e^{\pm iz}U\left(\nu+\tfrac{1}{2},2\nu+1,\mp 2iz\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)}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
