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Statements
M
κ
,
μ
(
x
)
=
Γ
(
2
μ
+
1
)
(
e
2
κ
2
-
μ
2
)
1
2
μ
(
κ
-
μ
κ
+
μ
)
1
2
κ
Ψ
(
κ
,
μ
,
x
)
(
J
2
μ
(
ζ
κ
)
+
env
J
2
μ
(
ζ
κ
)
O
(
κ
-
1
)
)
,
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑥
Euler-Gamma
2
𝜇
1
superscript
superscript
𝑒
2
superscript
𝜅
2
superscript
𝜇
2
1
2
𝜇
superscript
𝜅
𝜇
𝜅
𝜇
1
2
𝜅
Ψ
𝜅
𝜇
𝑥
Bessel-J
2
𝜇
𝜁
𝜅
envelope-Bessel-J
2
𝜇
𝜁
𝜅
Big-O
superscript
𝜅
1
{\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\Gamma\left(2\mu+1%
\right)\*\left(\frac{e^{2}}{\kappa^{2}-\mu^{2}}\right)^{\frac{1}{2}\mu}\*\left%
(\frac{\kappa-\mu}{\kappa+\mu}\right)^{\frac{1}{2}\kappa}\*\Psi(\kappa,\mu,x)%
\*\left(J_{2\mu}\left(\sqrt{\zeta\kappa}\right)+\mathrm{env}\mskip-2.0mu J_{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)}}
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)}}
env
J
ν
(
x
)
envelope-Bessel-J
𝜈
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar%
{x}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
x
𝑥
{\displaystyle{\displaystyle x}}
Ψ
(
κ
,
μ
,
x
)
Ψ
𝜅
𝜇
𝑥
{\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}
Identifiers
