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Statements
(
1
+
x
2
)
n
=
(
β
+
1
)
n
(
α
+
β
+
2
)
n
∑
ℓ
=
0
n
α
+
β
+
2
ℓ
+
1
α
+
β
+
1
(
α
+
β
+
1
)
ℓ
(
n
-
ℓ
+
1
)
ℓ
(
β
+
1
)
ℓ
(
n
+
α
+
β
+
2
)
ℓ
P
ℓ
(
α
,
β
)
(
x
)
,
superscript
1
𝑥
2
𝑛
Pochhammer
𝛽
1
𝑛
Pochhammer
𝛼
𝛽
2
𝑛
superscript
subscript
ℓ
0
𝑛
𝛼
𝛽
2
ℓ
1
𝛼
𝛽
1
Pochhammer
𝛼
𝛽
1
ℓ
Pochhammer
𝑛
ℓ
1
ℓ
Pochhammer
𝛽
1
ℓ
Pochhammer
𝑛
𝛼
𝛽
2
ℓ
Jacobi-polynomial-P
𝛼
𝛽
ℓ
𝑥
{\displaystyle{\displaystyle\left(\frac{1+x}{2}\right)^{n}=\frac{{\left(\beta+%
1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\frac{\alpha%
+\beta+2\ell+1}{\alpha+\beta+1}\frac{{\left(\alpha+\beta+1\right)_{\ell}}{%
\left(n-\ell+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+%
\beta+2\right)_{\ell}}}P^{(\alpha,\beta)}_{\ell}\left(x\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)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
