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Statements
∫
0
∞
t
exp
(
-
p
2
t
2
)
I
ν
(
a
t
)
I
ν
(
b
t
)
d
t
=
1
2
p
2
exp
(
a
2
+
b
2
4
p
2
)
I
ν
(
a
b
2
p
2
)
,
superscript
subscript
0
𝑡
superscript
𝑝
2
superscript
𝑡
2
modified-Bessel-first-kind
𝜈
𝑎
𝑡
modified-Bessel-first-kind
𝜈
𝑏
𝑡
𝑡
1
2
superscript
𝑝
2
superscript
𝑎
2
superscript
𝑏
2
4
superscript
𝑝
2
modified-Bessel-first-kind
𝜈
𝑎
𝑏
2
superscript
𝑝
2
{\displaystyle{\displaystyle\int_{0}^{\infty}t\exp\left(-p^{2}t^{2}\right)I_{%
\nu}\left(at\right)I_{\nu}\left(bt\right)\mathrm{d}t=\frac{1}{2p^{2}}\exp\left%
(\frac{a^{2}+b^{2}}{4p^{2}}\right)I_{\nu}\left(\frac{ab}{2p^{2}}\right),}}
ℜ
ν
>
-
1
,
ℜ
(
p
2
)
>
0
formulae-sequence
𝜈
1
superscript
𝑝
2
0
{\displaystyle{\displaystyle\Re\nu>-1,\Re\left(p^{2}\right)>0}}
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
