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