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Statements
W
-
κ
,
μ
(
x
e
-
π
i
)
=
π
x
Γ
(
κ
+
1
2
)
e
μ
π
i
(
H
2
μ
(
1
)
(
2
x
κ
)
+
env
Y
2
μ
(
2
x
κ
)
O
(
κ
-
1
2
)
)
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑥
superscript
𝑒
𝜋
imaginary-unit
𝜋
𝑥
Euler-Gamma
𝜅
1
2
superscript
𝑒
𝜇
𝜋
imaginary-unit
Hankel-H-1-Bessel-third-kind
2
𝜇
2
𝑥
𝜅
envelope-Bessel-Y
2
𝜇
2
𝑥
𝜅
Big-O
superscript
𝜅
1
2
{\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=%
\frac{\pi\sqrt{x}}{\Gamma\left(\kappa+\tfrac{1}{2}\right)}e^{\mu\pi\mathrm{i}}%
\*\left({H^{(1)}_{2\mu}}\left(2\sqrt{x\kappa}\right)+\mathrm{env}\mskip-2.0mu %
Y_{2\mu}\left(2\sqrt{x\kappa}\right)O\left(\kappa^{-\frac{1}{2}}\right)\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)}}
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}}
Identifiers
