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Statements
K
n
(
z
)
=
(
-
1
)
n
-
1
2
(
∂
I
ν
(
z
)
∂
ν
|
ν
=
n
+
∂
I
ν
(
z
)
∂
ν
|
ν
=
-
n
)
,
modified-Bessel-second-kind
𝑛
𝑧
superscript
1
𝑛
1
2
evaluated-at
partial-derivative
modified-Bessel-first-kind
𝜈
𝑧
𝜈
𝜈
𝑛
evaluated-at
partial-derivative
modified-Bessel-first-kind
𝜈
𝑧
𝜈
𝜈
𝑛
{\displaystyle{\displaystyle K_{n}\left(z\right)=\frac{(-1)^{n-1}}{2}\*\left(%
\left.\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}+\left.%
\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=-n}\right),}}
n
=
0
,
±
1
,
±
2
,
…
𝑛
0
plus-or-minus
1
plus-or-minus
2
…
{\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}}
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)}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
