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Statements
M
(
a
,
b
,
z
)
∼
b
1
2
a
e
1
4
ζ
2
b
(
λ
(
λ
-
1
ζ
)
a
-
1
U
(
a
-
1
2
,
-
ζ
b
)
+
(
λ
(
λ
-
1
ζ
)
a
-
1
-
(
ζ
λ
-
1
)
a
)
U
(
a
-
3
2
,
-
ζ
b
)
ζ
b
)
asymptotically-equals
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑧
superscript
𝑏
1
2
𝑎
superscript
𝑒
1
4
superscript
𝜁
2
𝑏
𝜆
superscript
𝜆
1
𝜁
𝑎
1
parabolic-U
𝑎
1
2
𝜁
𝑏
𝜆
superscript
𝜆
1
𝜁
𝑎
1
superscript
𝜁
𝜆
1
𝑎
parabolic-U
𝑎
3
2
𝜁
𝑏
𝜁
𝑏
{\displaystyle{\displaystyle M\left(a,b,z\right)\sim b^{\frac{1}{2}a}e^{\frac{%
1}{4}\zeta^{2}b}\left(\lambda\left(\frac{\lambda-1}{\zeta}\right)^{a-1}U\left(%
a-\tfrac{1}{2},-\zeta\sqrt{b}\right)+\left(\lambda\left(\frac{\lambda-1}{\zeta%
}\right)^{a-1}-\left(\frac{\zeta}{\lambda-1}\right)^{a}\right)\frac{U\left(a-%
\tfrac{3}{2},-\zeta\sqrt{b}\right)}{\zeta\sqrt{b}}\right)}}
M
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
∼
asymptotically-equals
{\displaystyle{\displaystyle\sim}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
