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Statements
∫
0
∞
J
ν
(
b
t
)
exp
(
-
p
2
t
2
)
d
t
=
π
2
p
exp
(
-
b
2
8
p
2
)
I
ν
/
2
(
b
2
8
p
2
)
,
superscript
subscript
0
Bessel-J
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
2
superscript
𝑏
2
8
superscript
𝑝
2
{\displaystyle{\displaystyle\int_{0}^{\infty}J_{\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)I_{\ifrac{\nu}{2}}\left(\frac{b^{2}}{8p^{2}}\right),}}
ℜ
ν
>
-
1
,
ℜ
(
p
2
)
>
0
formulae-sequence
𝜈
1
superscript
𝑝
2
0
{\displaystyle{\displaystyle\Re\nu>-1,\Re(p^{2})>0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\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)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
