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Statements
K
ν
(
z
)
=
{
1
2
π
i
e
ν
π
i
/
2
H
ν
(
1
)
(
z
e
π
i
/
2
)
,
-
π
≤
ph
z
≤
1
2
π
,
-
1
2
π
i
e
-
ν
π
i
/
2
H
ν
(
2
)
(
z
e
-
π
i
/
2
)
,
-
1
2
π
≤
ph
z
≤
π
.
modified-Bessel-second-kind
𝜈
𝑧
cases
1
2
𝜋
𝑖
superscript
𝑒
𝜈
𝜋
𝑖
2
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
superscript
𝑒
𝜋
𝑖
2
𝜋
phase
𝑧
1
2
𝜋
1
2
𝜋
𝑖
superscript
𝑒
𝜈
𝜋
𝑖
2
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
superscript
𝑒
𝜋
𝑖
2
1
2
𝜋
phase
𝑧
𝜋
{\displaystyle{\displaystyle K_{\nu}\left(z\right)=\begin{cases}\tfrac{1}{2}%
\pi ie^{\nu\pi i/2}{H^{(1)}_{\nu}}\left(ze^{\pi i/2}\right),&-\pi\leq%
\operatorname{ph}z\leq\tfrac{1}{2}\pi,\\
-\tfrac{1}{2}\pi ie^{-\nu\pi i/2}{H^{(2)}_{\nu}}\left(ze^{-\pi i/2}\right),&-%
\tfrac{1}{2}\pi\leq\operatorname{ph}z\leq\pi.\end{cases}}}
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)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
