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Statements
(
1
-
x
)
α
+
μ
P
n
(
α
+
μ
,
β
-
μ
)
(
x
)
Γ
(
α
+
μ
+
n
+
1
)
=
∫
x
1
(
1
-
y
)
α
P
n
(
α
,
β
)
(
y
)
Γ
(
α
+
n
+
1
)
(
y
-
x
)
μ
-
1
Γ
(
μ
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d
y
,
superscript
1
𝑥
𝛼
𝜇
Jacobi-polynomial-P
𝛼
𝜇
𝛽
𝜇
𝑛
𝑥
Euler-Gamma
𝛼
𝜇
𝑛
1
superscript
subscript
𝑥
1
superscript
1
𝑦
𝛼
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑦
Euler-Gamma
𝛼
𝑛
1
superscript
𝑦
𝑥
𝜇
1
Euler-Gamma
𝜇
𝑦
{\displaystyle{\displaystyle\frac{(1-x)^{\alpha+\mu}P^{(\alpha+\mu,\beta-\mu)}%
_{n}\left(x\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{x}^{1}\frac{(1-y)%
^{\alpha}P^{(\alpha,\beta)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}%
\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y,}}
-
1
<
x
<
1
1
𝑥
1
{\displaystyle{\displaystyle-1<x<1}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
n
(
α
,
β
)
(
x
)
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\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
