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Statements
K
ν
(
x
z
)
=
Γ
(
ν
+
1
2
)
(
2
z
)
ν
π
1
2
x
ν
∫
0
∞
cos
(
x
t
)
d
t
(
t
2
+
z
2
)
ν
+
1
2
,
modified-Bessel-second-kind
𝜈
𝑥
𝑧
Euler-Gamma
𝜈
1
2
superscript
2
𝑧
𝜈
superscript
𝜋
1
2
superscript
𝑥
𝜈
superscript
subscript
0
𝑥
𝑡
𝑡
superscript
superscript
𝑡
2
superscript
𝑧
2
𝜈
1
2
{\displaystyle{\displaystyle K_{\nu}\left(xz\right)=\frac{\Gamma\left(\nu+%
\frac{1}{2}\right)(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{%
\cos\left(xt\right)\mathrm{d}t}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}},}}
ℜ
ν
>
-
1
2
𝜈
1
2
{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
ℜ
ν
>
-
1
2
𝜈
1
2
{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
|
ph
z
|
<
1
2
π
ph
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
