Geodesic
Orthogonal polynomials related to the oscillatory-chebyshev weight function
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005) no. 1
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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 
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     title = {Orthogonal polynomials related to the oscillatory-chebyshev weight function},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {47 - 60},
     year = {2005},
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G. V. Milovanović; A. S. Cvetković. Orthogonal polynomials related to the oscillatory-chebyshev weight function. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005) no. 1. http://geodesic.mathdoc.fr/item/BASS_2005_30_1_a3/