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Statements
M
κ
,
μ
(
x
)
=
(
8
μ
)
1
4
(
2
μ
e
)
2
μ
(
e
κ
+
μ
)
1
2
(
κ
+
μ
)
Φ
(
κ
,
μ
,
x
)
(
U
(
μ
-
κ
,
-
ζ
2
μ
)
+
env
U
(
μ
-
κ
,
-
ζ
2
μ
)
O
(
μ
-
2
3
)
)
,
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑥
superscript
8
𝜇
1
4
superscript
2
𝜇
𝑒
2
𝜇
superscript
𝑒
𝜅
𝜇
1
2
𝜅
𝜇
Φ
𝜅
𝜇
𝑥
parabolic-U
𝜇
𝜅
𝜁
2
𝜇
envelope-Parabolic-U
𝜇
𝜅
𝜁
2
𝜇
Big-O
superscript
𝜇
2
3
{\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\left(8\mu\right)^{%
\frac{1}{4}}\*\left(\frac{2\mu}{e}\right)^{2\mu}\*\left(\frac{e}{\kappa+\mu}%
\right)^{\frac{1}{2}(\kappa+\mu)}\*\Phi(\kappa,\mu,x)\*\left(U\left(\mu-\kappa%
,-\zeta\sqrt{2\mu}\right)+\mathrm{env}\mskip-1.0mu U\left(\mu-\kappa,-\zeta%
\sqrt{2\mu}\right)O\left(\mu^{-\frac{2}{3}}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
env
U
(
c
,
x
)
envelope-Parabolic-U
𝑐
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}%
\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
Φ
(
κ
,
μ
,
x
)
Φ
𝜅
𝜇
𝑥
{\displaystyle{\displaystyle\Phi(\kappa,\mu,x)}}
Identifiers
