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Statements
∫
0
∞
Y
2
ν
(
b
t
)
exp
(
-
p
2
t
2
)
d
t
=
-
π
2
p
exp
(
-
b
2
8
p
2
)
(
I
ν
(
b
2
8
p
2
)
tan
(
ν
π
)
+
1
π
K
ν
(
b
2
8
p
2
)
sec
(
ν
π
)
)
,
superscript
subscript
0
Bessel-Y-Weber
2
𝜈
𝑏
𝑡
superscript
𝑝
2
superscript
𝑡
2
𝑡
𝜋
2
𝑝
superscript
𝑏
2
8
superscript
𝑝
2
modified-Bessel-first-kind
𝜈
superscript
𝑏
2
8
superscript
𝑝
2
𝜈
𝜋
1
𝜋
modified-Bessel-second-kind
𝜈
superscript
𝑏
2
8
superscript
𝑝
2
𝜈
𝜋
{\displaystyle{\displaystyle\int_{0}^{\infty}Y_{2\nu}\left(bt\right)\exp\left(%
-p^{2}t^{2}\right)\mathrm{d}t=-\frac{\sqrt{\pi}}{2p}\exp\left(-\frac{b^{2}}{8p%
^{2}}\right)\left(I_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\tan\left(\nu\pi%
\right)+\frac{1}{\pi}K_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\sec\left(\nu\pi%
\right)\right),}}
|
ℜ
ν
|
<
1
2
𝜈
1
2
{\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}
ℜ
(
p
2
)
>
0
superscript
𝑝
2
0
{\displaystyle{\displaystyle\Re(p^{2})>0}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
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)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sec
z
𝑧
{\displaystyle{\displaystyle\sec\NVar{z}}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
