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DLMF:18.7.E13
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Formula:6278
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MaRDI QID
Q6278
Label: DLMF:18.7.E13
Digital Library of Mathematical Functions ID
18.7.E13
P
2
n
(
α
,
α
)
(
x
)
P
2
n
(
α
,
α
)
(
1
)
=
P
n
(
α
,
-
1
2
)
(
2
x
2
-
1
)
P
n
(
α
,
-
1
2
)
(
1
)
,
Jacobi-polynomial-P
𝛼
𝛼
2
𝑛
𝑥
Jacobi-polynomial-P
𝛼
𝛼
2
𝑛
1
Jacobi-polynomial-P
𝛼
1
2
𝑛
2
superscript
𝑥
2
1
Jacobi-polynomial-P
𝛼
1
2
𝑛
1
{\displaystyle{\displaystyle\frac{P^{(\alpha,\alpha)}_{2n}\left(x\right)}{P^{(% \alpha,\alpha)}_{2n}\left(1\right)}=\frac{P^{(\alpha,-\frac{1}{2})}_{n}\left(2% x^{2}-1\right)}{P^{(\alpha,-\frac{1}{2})}_{n}\left(1\right)},}}
Constraint(s)
Symbols List
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)}}
: Jacobi polynomial
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
x
𝑥
{\displaystyle{\displaystyle x}}
: real variable
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