Abstract
Abstract
If μk,n
(α,β) denotes the relative extrema of the
Jacobi polynomial P(α,β)
n(x), ordered so that
μ
k+1,n
(α,β) lies to the left of μ
k,n
(α,β), then R. A. Askey has conjectured
twenty years ago that for
for k = 1,…,
n — 1 and n = 1,2,=. In
this paper, we give an asymptotic expansion for μ
k,n
(α,β) when k is
fixed and n → ∞, which corrects an earlier result of R.
Cooper (1950). Furthermore, we show that Askey's conjecture is true at least in
the asymptotic sense.
Publisher
Canadian Mathematical Society
Cited by
19 articles.
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1. Index;Encyclopedia of Special Functions: The Askey-Bateman Project;2020-09-30
2. Some Families of Matrix-Valued Jacobi Orthogonal Polynomials;Encyclopedia of Special Functions: The Askey-Bateman Project;2020-09-30
3. Matrix-Valued Orthogonal Polynomials and Differential Equations;Encyclopedia of Special Functions: The Askey-Bateman Project;2020-09-30
4. The Moment Problem;Encyclopedia of Special Functions: The Askey-Bateman Project;2020-09-30
5. Zeros of Orthogonal Polynomials;Encyclopedia of Special Functions: The Askey-Bateman Project;2020-09-30