EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXI, No. 30, pp. 47–60 (2005)

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Orthogonal polynomials related to the oscillatory-Chebyshev weight function

G. V. Milovanovic and A. S. Cvetkovic

Department Mathematics, Faculty of Electronic Engineering, University of Nis, P. O. Box 73, 18000 Nis, Serbia and Montenegro

Abstract: In this paper we discuss the existence question for polynomials orthogonal with respect to the moment functional
L(p)=\int_{-1}^1 p(x) x (1-x^2)^{-1/2}e^{\ij \zeta x} d x,\quad \zeta\in \RR.
Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived.

Keywords: Orthogonal polynomials; Moments; Moment functional; Three-term recurrence relation; Oscillatory Chebyshev weight; Asymptotic formulae; Bessel functions

Classification (MSC2000): 30C10, 33C47

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Electronic fulltext finalized on: 21 Nov 2005. This page was last modified: 20 Jun 2011.

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