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Statements
W
κ
,
μ
(
x
)
=
2
π
κ
1
6
(
κ
+
μ
κ
-
μ
)
1
2
μ
(
κ
2
-
μ
2
e
2
)
1
2
κ
Ψ
^
(
κ
,
μ
,
x
)
(
Ai
(
κ
2
3
ζ
^
)
+
envAi
(
κ
2
3
ζ
^
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑥
2
𝜋
superscript
𝜅
1
6
superscript
𝜅
𝜇
𝜅
𝜇
1
2
𝜇
superscript
superscript
𝜅
2
superscript
𝜇
2
superscript
𝑒
2
1
2
𝜅
^
Ψ
𝜅
𝜇
𝑥
Airy-Ai
superscript
𝜅
2
3
^
𝜁
envelope-Airy-Ai
superscript
𝜅
2
3
^
𝜁
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{2\pi}\kappa^{%
\frac{1}{6}}\*\left(\frac{\kappa+\mu}{\kappa-\mu}\right)^{\frac{1}{2}\mu}\*%
\left(\frac{\kappa^{2}-\mu^{2}}{e^{2}}\right)^{\frac{1}{2}\kappa}\*\widehat{%
\Psi}(\kappa,\mu,x)\*\left(\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta%
}\right)+\mathrm{envAi}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)O\left(%
\kappa^{-1}\right)\right),}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\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)}}
π
{\displaystyle{\displaystyle\pi}}
envAi
(
x
)
envelope-Airy-Ai
𝑥
{\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
x
𝑥
{\displaystyle{\displaystyle x}}
Ψ
^
(
κ
,
μ
,
x
)
^
Ψ
𝜅
𝜇
𝑥
{\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}
