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