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), p. 47 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
DOI : 10.2298/BMAT0530047M
Classification : 30C10 33C47
Keywords: Orthogonal polynomials, Moments, Moment functional, Three-term recurrence relation, Oscillatory Chebyshev weight, Asymptotic formulae, Bessel functions 
@article{10_2298_BMAT0530047M,
     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 },
     publisher = {mathdoc},
     volume = {30},
     year = {2005},
     doi = {10.2298/BMAT0530047M},
     zbl = {1249.30010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530047M/}
}
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 
VL  - 30
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530047M/
DO  - 10.2298/BMAT0530047M
LA  - en
ID  - 10_2298_BMAT0530047M
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 
%V 30
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530047M/
%R 10.2298/BMAT0530047M
%G en
%F 10_2298_BMAT0530047M
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), p. 47 . doi : 10.2298/BMAT0530047M. http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530047M/

Cité par Sources :