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Statements
W
κ
,
μ
(
x
)
=
e
-
μ
π
i
π
Γ
(
κ
+
μ
+
1
2
)
Γ
(
κ
-
μ
+
1
2
)
c
(
κ
,
μ
)
Ψ
(
κ
,
μ
,
x
)
(
sin
(
κ
π
-
μ
π
)
J
2
μ
(
ζ
κ
)
-
cos
(
κ
π
-
μ
π
)
Y
2
μ
(
ζ
κ
)
+
env
Y
2
μ
(
ζ
κ
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑥
superscript
𝑒
𝜇
𝜋
imaginary-unit
𝜋
Euler-Gamma
𝜅
𝜇
1
2
Euler-Gamma
𝜅
𝜇
1
2
𝑐
𝜅
𝜇
Ψ
𝜅
𝜇
𝑥
𝜅
𝜋
𝜇
𝜋
Bessel-J
2
𝜇
𝜁
𝜅
𝜅
𝜋
𝜇
𝜋
Bessel-Y-Weber
2
𝜇
𝜁
𝜅
envelope-Bessel-Y
2
𝜇
𝜁
𝜅
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\frac{e^{-\mu\pi%
\mathrm{i}}}{\pi}\Gamma\left(\kappa+\mu+\tfrac{1}{2}\right)\*\Gamma\left(%
\kappa-\mu+\tfrac{1}{2}\right)\*c(\kappa,\mu)\Psi(\kappa,\mu,x)\*\left(\sin%
\left(\kappa\pi-\mu\pi\right)J_{2\mu}\left(\sqrt{\zeta\kappa}\right)-\cos\left%
(\kappa\pi-\mu\pi\right)Y_{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),}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\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)}}
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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
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}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
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
