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Statements
ker
ν
x
+
i
kei
ν
x
=
e
-
ν
π
i
/
2
K
ν
(
x
e
π
i
/
4
)
=
1
2
π
i
H
ν
(
1
)
(
x
e
3
π
i
/
4
)
=
-
1
2
π
i
e
-
ν
π
i
H
ν
(
2
)
(
x
e
-
π
i
/
4
)
.
Kelvin-ker
𝜈
𝑥
𝑖
Kelvin-kei
𝜈
𝑥
superscript
𝑒
𝜈
𝜋
𝑖
2
modified-Bessel-second-kind
𝜈
𝑥
superscript
𝑒
𝜋
𝑖
4
1
2
𝜋
𝑖
Hankel-H-1-Bessel-third-kind
𝜈
𝑥
superscript
𝑒
3
𝜋
𝑖
4
1
2
𝜋
𝑖
superscript
𝑒
𝜈
𝜋
𝑖
Hankel-H-2-Bessel-third-kind
𝜈
𝑥
superscript
𝑒
𝜋
𝑖
4
{\displaystyle{\displaystyle\operatorname{ker}_{\nu}x+i\operatorname{kei}_{\nu%
}x=e^{-\nu\pi i/2}K_{\nu}\left(xe^{\pi i/4}\right)=\tfrac{1}{2}\pi i{H^{(1)}_{%
\nu}}\left(xe^{3\pi i/4}\right)=-\tfrac{1}{2}\pi ie^{-\nu\pi i}{H^{(2)}_{\nu}}%
\left(xe^{-\pi i/4}\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)}}
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)}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
