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Statements
P
n
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α
,
β
)
(
x
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P
n
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α
,
β
)
(
1
)
P
n
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α
,
β
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(
y
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P
n
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α
,
β
)
(
1
)
=
∑
ℓ
=
0
n
b
n
,
ℓ
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x
+
y
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ℓ
P
ℓ
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α
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β
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(
(
1
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x
y
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/
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x
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y
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P
ℓ
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α
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β
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(
1
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,
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
Jacobi-polynomial-P
𝛼
𝛽
𝑛
1
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑦
Jacobi-polynomial-P
𝛼
𝛽
𝑛
1
superscript
subscript
ℓ
0
𝑛
subscript
𝑏
𝑛
ℓ
superscript
𝑥
𝑦
ℓ
Jacobi-polynomial-P
𝛼
𝛽
ℓ
1
𝑥
𝑦
𝑥
𝑦
Jacobi-polynomial-P
𝛼
𝛽
ℓ
1
{\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(%
\alpha,\beta)}_{n}\left(1\right)}\frac{P^{(\alpha,\beta)}_{n}\left(y\right)}{P%
^{(\alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+y)^{\ell}\*%
\frac{P^{(\alpha,\beta)}_{\ell}\left(\ifrac{(1+xy)}{(x+y)}\right)}{P^{(\alpha,%
\beta)}_{\ell}\left(1\right)},}}
P
n
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α
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β
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x
)
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(%
\NVar{x}\right)}}
y
𝑦
{\displaystyle{\displaystyle y}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
