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Statements
x
α
+
μ
L
n
(
α
+
μ
)
(
x
)
Γ
(
α
+
μ
+
n
+
1
)
=
∫
0
x
y
α
L
n
(
α
)
(
y
)
Γ
(
α
+
n
+
1
)
(
x
-
y
)
μ
-
1
Γ
(
μ
)
d
y
,
superscript
𝑥
𝛼
𝜇
Laguerre-polynomial-L
𝛼
𝜇
𝑛
𝑥
Euler-Gamma
𝛼
𝜇
𝑛
1
superscript
subscript
0
𝑥
superscript
𝑦
𝛼
Laguerre-polynomial-L
𝛼
𝑛
𝑦
Euler-Gamma
𝛼
𝑛
1
superscript
𝑥
𝑦
𝜇
1
Euler-Gamma
𝜇
𝑦
{\displaystyle{\displaystyle\frac{x^{\alpha+\mu}L^{(\alpha+\mu)}_{n}\left(x%
\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{0}^{x}\frac{y^{\alpha}L^{(%
\alpha)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}\frac{(x-y)^{\mu-1}}%
{\Gamma\left(\mu\right)}\mathrm{d}y,}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
L
n
(
α
)
(
x
)
Laguerre-polynomial-L
𝛼
𝑛
𝑥
{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}%
\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
y
𝑦
{\displaystyle{\displaystyle y}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
