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Statements
π
β‘
(
a
,
b
,
-
z
)
=
z
1
2
-
1
2
β’
b
Ξ
β‘
(
a
)
β’
β«
0
β
e
-
t
β’
t
a
-
1
2
β’
b
-
1
2
β’
J
b
-
1
β‘
(
2
β’
z
β’
t
)
β’
d
t
,
Kummer-confluent-hypergeometric-bold-M
π
π
π§
superscript
π§
1
2
1
2
π
Euler-Gamma
π
superscript
subscript
0
superscript
π
π‘
superscript
π‘
π
1
2
π
1
2
Bessel-J
π
1
2
π§
π‘
π‘
{\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{z^{\frac{1}{%
2}-\frac{1}{2}b}}{\Gamma\left(a\right)}\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}%
b-\frac{1}{2}}J_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t,}}
β
β‘
a
>
0
π
0
{\displaystyle{\displaystyle\Re a>0}}
J
Ξ½
β‘
(
z
)
Bessel-J
π
π§
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
β‘
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-bold-M
π
π
π§
{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right%
)}}
d
x
π₯
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
β«
{\displaystyle{\displaystyle\int}}
β
β‘
absent
{\displaystyle{\displaystyle\Re}}
z
π§
{\displaystyle{\displaystyle z}}
Identifiers
