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DLMF:18.9.E3
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Formula:6296
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MaRDI QID
Q6296
Label: DLMF:18.9.E3
Digital Library of Mathematical Functions ID
18.9.E3
P
n
(
α
,
β
-
1
)
(
x
)
-
P
n
(
α
-
1
,
β
)
(
x
)
=
P
n
-
1
(
α
,
β
)
(
x
)
,
Jacobi-polynomial-P
𝛼
𝛽
1
𝑛
𝑥
Jacobi-polynomial-P
𝛼
1
𝛽
𝑛
𝑥
Jacobi-polynomial-P
𝛼
𝛽
𝑛
1
𝑥
{\displaystyle{\displaystyle P^{(\alpha,\beta-1)}_{n}\left(x\right)-P^{(\alpha% -1,\beta)}_{n}\left(x\right)=P^{(\alpha,\beta)}_{n-1}\left(x\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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