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DLMF:18.7.E6
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Formula:6271
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MaRDI QID
Q6271
Label: DLMF:18.7.E6
Digital Library of Mathematical Functions ID
18.7.E6
W
n
(
x
)
=
P
n
(
-
1
2
,
1
2
)
(
x
)
/
P
n
(
-
1
2
,
1
2
)
(
1
)
.
Chebyshev-polynomial-fourth-kind-W
𝑛
𝑥
Jacobi-polynomial-P
1
2
1
2
𝑛
𝑥
Jacobi-polynomial-P
1
2
1
2
𝑛
1
{\displaystyle{\displaystyle W_{n}\left(x\right)=\ifrac{P^{(-\frac{1}{2},\frac% {1}{2})}_{n}\left(x\right)}{P^{(-\frac{1}{2},\frac{1}{2})}_{n}\left(1\right)}.}}
Constraint(s)
Symbols List
W
n
(
x
)
Chebyshev-polynomial-fourth-kind-W
𝑛
𝑥
{\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x}\right)}}
: Chebyshev polynomial of the fourth kind
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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