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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 
@article{BASS_2005_30_1_a3,
     author = {G. V. Milovanovi\'c and A. S. Cvetkovi\'c},
     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},
     volume = {30},
     number = {1},
     zbl = {1249.30010},
     url = {http://geodesic.mathdoc.fr/item/BASS_2005_30_1_a3/}
}
TY  - JOUR
AU  - G. V. Milovanović
AU  - A. S. Cvetković
TI  - Orthogonal polynomials related to the oscillatory-chebyshev weight function
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2005
SP  - 47 
EP  -  60
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASS_2005_30_1_a3/
ID  - BASS_2005_30_1_a3
ER  - 
%0 Journal Article
%A G. V. Milovanović
%A A. S. Cvetković
%T Orthogonal polynomials related to the oscillatory-chebyshev weight function
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2005
%P 47 - 60
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2005_30_1_a3/
%F BASS_2005_30_1_a3
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/