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Statements
K
ν
(
ν
z
)
=
(
π
2
ν
)
1
2
e
-
ν
η
(
1
+
z
2
)
1
4
(
∑
k
=
0
ℓ
-
1
(
-
1
)
k
U
k
(
p
)
ν
k
+
O
(
1
z
ℓ
)
)
,
modified-Bessel-second-kind
𝜈
𝜈
𝑧
superscript
𝜋
2
𝜈
1
2
superscript
𝑒
𝜈
𝜂
superscript
1
superscript
𝑧
2
1
4
superscript
subscript
𝑘
0
ℓ
1
superscript
1
𝑘
subscript
𝑈
𝑘
𝑝
superscript
𝜈
𝑘
Big-O
1
superscript
𝑧
ℓ
{\displaystyle{\displaystyle K_{\nu}\left(\nu z\right)=\left(\frac{\pi}{2\nu}%
\right)^{\frac{1}{2}}\frac{e^{-\nu\eta}}{(1+z^{2})^{\frac{1}{4}}}\*\left(\sum_%
{k=0}^{\ell-1}(-1)^{k}\frac{U_{k}(p)}{\nu^{k}}+O\left(\frac{1}{z^{\ell}}\right%
)\right),}}
|
ph
z
|
≤
3
2
π
-
δ
phase
𝑧
3
2
𝜋
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
p
𝑝
{\displaystyle{\displaystyle p}}
U
k
(
p
)
subscript
𝑈
𝑘
𝑝
{\displaystyle{\displaystyle U_{k}(p)}}
Identifiers
