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Statements
K
ν
(
z
e
m
π
i
)
=
e
-
m
ν
π
i
K
ν
(
z
)
-
π
i
sin
(
m
ν
π
)
csc
(
ν
π
)
I
ν
(
z
)
.
modified-Bessel-second-kind
𝜈
𝑧
superscript
𝑒
𝑚
𝜋
𝑖
superscript
𝑒
𝑚
𝜈
𝜋
𝑖
modified-Bessel-second-kind
𝜈
𝑧
𝜋
𝑖
𝑚
𝜈
𝜋
𝜈
𝜋
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\nu}\left(ze^{m\pi i}\right)=e^{-m\nu\pi i}K_{%
\nu}\left(z\right)-\pi i\sin\left(m\nu\pi\right)\csc\left(\nu\pi\right)I_{\nu}%
\left(z\right).}}
π
{\displaystyle{\displaystyle\pi}}
csc
z
𝑧
{\displaystyle{\displaystyle\csc\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
