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Statements
W
κ
,
μ
(
x
)
=
(
1
2
μ
)
-
1
4
(
κ
+
μ
e
)
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-W
𝜅
𝜇
𝑥
superscript
1
2
𝜇
1
4
superscript
𝜅
𝜇
𝑒
1
2
𝜅
𝜇
Φ
𝜅
𝜇
𝑥
parabolic-U
𝜇
𝜅
𝜁
2
𝜇
envelope-Parabolic-U-bar
𝜇
𝜅
𝜁
2
𝜇
Big-O
superscript
𝜇
2
3
{\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\left(\tfrac{1}{2}%
\mu\right)^{-\frac{1}{4}}\*\left(\frac{\kappa+\mu}{e}\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 \overline{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)}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
env
U
¯
(
c
,
x
)
envelope-Parabolic-U-bar
𝑐
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu \overline{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
