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Statements
x
β
+
μ
(
x
+
1
)
n
Γ
(
β
+
μ
+
n
+
1
)
P
n
(
α
,
β
+
μ
)
(
x
-
1
x
+
1
)
=
∫
0
x
y
β
(
y
+
1
)
n
Γ
(
β
+
n
+
1
)
P
n
(
α
,
β
)
(
y
-
1
y
+
1
)
(
x
-
y
)
μ
-
1
Γ
(
μ
)
d
y
,
superscript
𝑥
𝛽
𝜇
superscript
𝑥
1
𝑛
Euler-Gamma
𝛽
𝜇
𝑛
1
Jacobi-polynomial-P
𝛼
𝛽
𝜇
𝑛
𝑥
1
𝑥
1
superscript
subscript
0
𝑥
superscript
𝑦
𝛽
superscript
𝑦
1
𝑛
Euler-Gamma
𝛽
𝑛
1
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑦
1
𝑦
1
superscript
𝑥
𝑦
𝜇
1
Euler-Gamma
𝜇
𝑦
{\displaystyle{\displaystyle\frac{x^{\beta+\mu}(x+1)^{n}}{\Gamma\left(\beta+%
\mu+n+1\right)}P^{(\alpha,\beta+\mu)}_{n}\left(\frac{x-1}{x+1}\right)=\int_{0}%
^{x}\frac{y^{\beta}(y+1)^{n}}{\Gamma\left(\beta+n+1\right)}P^{(\alpha,\beta)}_%
{n}\left(\frac{y-1}{y+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)}}
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
