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Statements
π
β‘
(
-
a
,
b
,
z
)
βΌ
(
z
/
a
)
(
1
-
b
)
/
2
β’
e
z
/
2
β’
Ξ
β‘
(
1
+
a
)
Ξ
β‘
(
a
+
b
)
β’
(
J
b
-
1
β‘
(
2
β’
a
β’
z
)
β’
β
s
=
0
β
p
s
β’
(
z
)
(
-
a
)
s
-
z
/
a
β’
J
b
β‘
(
2
β’
a
β’
z
)
β’
β
s
=
0
β
q
s
β’
(
z
)
(
-
a
)
s
)
,
asymptotic-expansion
Kummer-confluent-hypergeometric-bold-M
π
π
π§
superscript
π§
π
1
π
2
superscript
π
π§
2
Euler-Gamma
1
π
Euler-Gamma
π
π
Bessel-J
π
1
2
π
π§
superscript
subscript
π
0
subscript
π
π
π§
superscript
π
π
π§
π
Bessel-J
π
2
π
π§
superscript
subscript
π
0
subscript
π
π
π§
superscript
π
π
{\displaystyle{\displaystyle{\mathbf{M}}\left(-a,b,z\right)\sim\left(z/a\right%
)^{(1-b)/2}\frac{e^{z/2}\Gamma\left(1+a\right)}{\Gamma\left(a+b\right)}\*\left%
(J_{b-1}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{p_{s}(z)}{(-a)^{s}}-%
\sqrt{z/a}J_{b}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{q_{s}(z)}{(-a)^%
{s}}\right),}}
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%
)}}
βΌ
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
s
π
{\displaystyle{\displaystyle s}}
z
π§
{\displaystyle{\displaystyle z}}
