View More View Less
  • 1 School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA
Restricted access

Abstract

Müntz–Legendre polynomials Ln(Λ;x) associated with a sequence Λ={λk} are obtained by orthogonalizing the system in L2[0,1] with respect to the Legendre weight. Under very mild conditions on Λ, we establish the endpoint asymptotics close to x=1. The main result is
ea
where and J0 is the Bessel function of order 0.
  • [1] Abramowitz, M. and Stegun, I. A. (Eds.), Bessel Functions Jand Y, §9.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, Dover (New York, 1972), pp. 358–364.

    • Search Google Scholar
    • Export Citation
  • [2] Borwein, P. B., Erdélyi, T. 1995 Polynomials and Polynomial Inequalities Springer New York.

  • [3] Borwein, P. B., Erdélyi, T., Zhang, J. 1994 Müntz systems and Müntz–Legendre polynomials Trans. Amer. Math. Soc. 342 523554 .

  • [4] Olver, F. W. J. 1997 Asymptotics and Special Functions A K Peters Natick.

  • [5] Stefánsson, Ú. F., Asymptotic behavior of Müntz orthogonal polynomials, Constructive Approximation, in print, doi: .

  • [6] Szegö, G. 1939 Orthogonal Polynomials AMS Coll. Publ. XXXIII Amer. Math. Soc. Providence.

Acta Mathematica Hungarica
P.O. Box 127
HU–1364 Budapest
Phone: (36 1) 483 8305
Fax: (36 1) 483 8333
E-mail: acta@renyi.mta.hu

  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

For subscription options, please visit the website of Springer Nature

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Feb 2021 0 0 0
Mar 2021 0 0 0
Apr 2021 0 0 0
May 2021 0 0 0
Jun 2021 0 0 0
Jul 2021 0 0 0
Aug 2021 0 0 0