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Statements
M
(
a
,
b
,
x
)
=
Γ
(
b
)
e
1
2
x
(
(
1
2
b
-
a
)
x
)
1
2
-
1
2
b
(
J
b
-
1
(
2
x
(
b
-
2
a
)
)
+
env
J
b
-
1
(
2
x
(
b
-
2
a
)
)
O
(
|
a
|
-
1
2
)
)
,
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑥
Euler-Gamma
𝑏
superscript
𝑒
1
2
𝑥
superscript
1
2
𝑏
𝑎
𝑥
1
2
1
2
𝑏
Bessel-J
𝑏
1
2
𝑥
𝑏
2
𝑎
envelope-Bessel-J
𝑏
1
2
𝑥
𝑏
2
𝑎
Big-O
𝑎
1
2
{\displaystyle{\displaystyle M\left(a,b,x\right)=\Gamma\left(b\right)e^{\frac{%
1}{2}x}\left((\tfrac{1}{2}b-a)x\right)^{\frac{1}{2}-\frac{1}{2}b}\*\left(J_{b-%
1}\left(\sqrt{2x(b-2a)}\right)+\mathrm{env}\mskip-2.0mu J_{b-1}\left(\sqrt{2x(%
b-2a)}\right)O\left({\left|a\right|^{-\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
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\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}}
Identifiers
