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Statements
M
κ
,
μ
(
x
)
=
1
2
π
Γ
(
2
μ
+
1
)
Γ
(
κ
-
μ
+
1
2
)
c
^
(
κ
,
μ
)
Ψ
^
(
κ
,
μ
,
x
)
(
sin
(
κ
π
-
μ
π
)
Ai
(
κ
2
3
ζ
^
)
+
cos
(
κ
π
-
μ
π
)
Bi
(
κ
2
3
ζ
^
)
+
envBi
(
κ
2
3
ζ
^
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑥
1
2
𝜋
Euler-Gamma
2
𝜇
1
Euler-Gamma
𝜅
𝜇
1
2
^
𝑐
𝜅
𝜇
^
Ψ
𝜅
𝜇
𝑥
𝜅
𝜋
𝜇
𝜋
Airy-Ai
superscript
𝜅
2
3
^
𝜁
𝜅
𝜋
𝜇
𝜋
Airy-Bi
superscript
𝜅
2
3
^
𝜁
envelope-Airy-Bi
superscript
𝜅
2
3
^
𝜁
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\frac{1}{2\pi}\*%
\Gamma\left(2\mu+1\right)\*\Gamma\left(\kappa-\mu+\tfrac{1}{2}\right)\*%
\widehat{c}(\kappa,\mu)\*\widehat{\Psi}(\kappa,\mu,x)\*\left(\sin\left(\kappa%
\pi-\mu\pi\right)\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)+%
\cos\left(\kappa\pi-\mu\pi\right)\mathrm{Bi}\left(\kappa^{\frac{2}{3}}\widehat%
{\zeta}\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)}}
Bi
(
z
)
Airy-Bi
𝑧
{\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
envBi
(
x
)
envelope-Airy-Bi
𝑥
{\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
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
