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Statements
L
n
(
α
)
(
x
)
=
n
1
2
α
-
1
4
e
1
2
x
π
1
2
x
1
2
α
+
1
4
(
cos
θ
n
(
α
)
(
x
)
(
∑
m
=
0
M
-
1
a
m
(
x
)
n
1
2
m
+
O
(
1
n
1
2
M
)
)
+
sin
θ
n
(
α
)
(
x
)
(
∑
m
=
1
M
-
1
b
m
(
x
)
n
1
2
m
+
O
(
1
n
1
2
M
)
)
)
,
Laguerre-polynomial-L
𝛼
𝑛
𝑥
superscript
𝑛
1
2
𝛼
1
4
superscript
𝑒
1
2
𝑥
superscript
𝜋
1
2
superscript
𝑥
1
2
𝛼
1
4
superscript
subscript
𝜃
𝑛
𝛼
𝑥
superscript
subscript
𝑚
0
𝑀
1
subscript
𝑎
𝑚
𝑥
superscript
𝑛
1
2
𝑚
Big-O
1
superscript
𝑛
1
2
𝑀
superscript
subscript
𝜃
𝑛
𝛼
𝑥
superscript
subscript
𝑚
1
𝑀
1
subscript
𝑏
𝑚
𝑥
superscript
𝑛
1
2
𝑚
Big-O
1
superscript
𝑛
1
2
𝑀
{\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\frac{n^{\frac{1}{%
2}\alpha-\frac{1}{4}}e^{\frac{1}{2}x}}{\pi^{\frac{1}{2}}x^{\frac{1}{2}\alpha+%
\frac{1}{4}}}\left(\cos\theta_{n}^{(\alpha)}(x)\left(\sum_{m=0}^{M-1}\frac{a_{%
m}(x)}{n^{\frac{1}{2}m}}+O\left(\frac{1}{n^{\frac{1}{2}M}}\right)\right)+\sin%
\theta_{n}^{(\alpha)}(x)\left(\sum_{m=1}^{M-1}\frac{b_{m}(x)}{n^{\frac{1}{2}m}%
}+O\left(\frac{1}{n^{\frac{1}{2}M}}\right)\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
L
n
(
α
)
(
x
)
Laguerre-polynomial-L
𝛼
𝑛
𝑥
{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
θ
n
(
α
)
(
x
)
superscript
subscript
𝜃
𝑛
𝛼
𝑥
{\displaystyle{\displaystyle\theta_{n}^{(\alpha)}(x)}}
a
m
(
x
)
subscript
𝑎
𝑚
𝑥
{\displaystyle{\displaystyle a_{m}(x)}}
b
m
(
x
)
subscript
𝑏
𝑚
𝑥
{\displaystyle{\displaystyle b_{m}(x)}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
