Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques   EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Académie Serbe des Sciences et des Arts, Beograd

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 Ni\v s, 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 version published on: 11 Apr 2006. This page was last modified: 13 Apr 2006.

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