Geodesic
Asymptotic Monotonicity of the Relative Extrema of Jacobi Polynomials
Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1318-1337

Voir la notice de l'article provenant de la source Cambridge University Press

If μk,n (α,β) denotes the relative extrema of the Jacobi polynomial P(α,β)n(x), ordered so thatμ k+1,n (α,β) lies to the left of μk,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.
DOI : 10.4153/CJM-1994-075-1
Mots-clés : 33C45, 41A60, Jacobi polynomials, zeros, relative extrema, uniform asymptotic approximation 
Wong, R.; Zhang, J.-M. Asymptotic Monotonicity of the Relative Extrema of Jacobi Polynomials. Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1318-1337. doi: 10.4153/CJM-1994-075-1
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