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Statements
W
-
κ
,
μ
(
x
e
-
π
i
)
=
c
(
κ
,
μ
)
Ψ
(
κ
,
μ
,
x
)
(
H
2
μ
(
1
)
(
ζ
κ
)
+
env
Y
2
μ
(
ζ
κ
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑥
superscript
𝑒
𝜋
imaginary-unit
𝑐
𝜅
𝜇
Ψ
𝜅
𝜇
𝑥
Hankel-H-1-Bessel-third-kind
2
𝜇
𝜁
𝜅
envelope-Bessel-Y
2
𝜇
𝜁
𝜅
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=c%
(\kappa,\mu)\Psi(\kappa,\mu,x)\left({H^{(1)}_{2\mu}}\left(\sqrt{\zeta\kappa}%
\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(\sqrt{\zeta\kappa}\right)O\left%
(\kappa^{-1}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\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}}
env
Y
ν
(
x
)
envelope-Bessel-Y
𝜈
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\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 c(\kappa,\mu)}}
Ψ
(
κ
,
μ
,
x
)
Ψ
𝜅
𝜇
𝑥
{\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}
Identifiers
