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Statements
W
-
κ
,
μ
(
x
e
π
i
)
=
e
-
(
κ
-
1
6
)
π
i
c
^
(
κ
,
μ
)
Ψ
^
(
κ
,
μ
,
x
)
(
Ai
(
κ
2
3
ζ
^
e
2
3
π
i
)
+
envBi
(
κ
2
3
ζ
^
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑥
superscript
𝑒
𝜋
imaginary-unit
superscript
𝑒
𝜅
1
6
𝜋
imaginary-unit
^
𝑐
𝜅
𝜇
^
Ψ
𝜅
𝜇
𝑥
Airy-Ai
superscript
𝜅
2
3
^
𝜁
superscript
𝑒
2
3
𝜋
imaginary-unit
envelope-Airy-Bi
superscript
𝜅
2
3
^
𝜁
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{\pi\mathrm{i}}\right)=e^%
{-(\kappa-\frac{1}{6})\pi\mathrm{i}}\widehat{c}(\kappa,\mu)\widehat{\Psi}(%
\kappa,\mu,x)\left(\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}e^{%
\frac{2}{3}\pi\mathrm{i}}\right)+\mathrm{envBi}\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}}
envBi
(
x
)
envelope-Airy-Bi
𝑥
{\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
x
𝑥
{\displaystyle{\displaystyle x}}
c
^
(
κ
,
μ
)
^
𝑐
𝜅
𝜇
{\displaystyle{\displaystyle\widehat{c}(\kappa,\mu)}}
Ψ
^
(
κ
,
μ
,
x
)
^
Ψ
𝜅
𝜇
𝑥
{\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}
Identifiers
