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Statements
∫
0
∞
t
exp
(
-
p
2
t
2
)
J
0
(
a
t
)
Y
0
(
a
t
)
d
t
=
-
1
2
π
p
2
exp
(
-
a
2
2
p
2
)
K
0
(
a
2
2
p
2
)
,
superscript
subscript
0
𝑡
superscript
𝑝
2
superscript
𝑡
2
Bessel-J
0
𝑎
𝑡
Bessel-Y-Weber
0
𝑎
𝑡
𝑡
1
2
𝜋
superscript
𝑝
2
superscript
𝑎
2
2
superscript
𝑝
2
modified-Bessel-second-kind
0
superscript
𝑎
2
2
superscript
𝑝
2
{\displaystyle{\displaystyle\int_{0}^{\infty}t\exp\left(-p^{2}t^{2}\right)J_{0%
}\left(at\right)Y_{0}\left(at\right)\mathrm{d}t=-\frac{1}{2\pi p^{2}}\exp\left%
(-\frac{a^{2}}{2p^{2}}\right)K_{0}\left(\frac{a^{2}}{2p^{2}}\right),}}
ℜ
(
p
2
)
>
0
superscript
𝑝
2
0
{\displaystyle{\displaystyle\Re(p^{2})>0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
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}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
Identifiers
