A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Mesk, Mohammed¹  Zahaf, Mohammed Brahim^2,3 

[1] Univ Tlemcen, Lab Anal Non Lineaire & Math Appl, BP 119, Tilimsen 13000, Algeria

[2] Univ Tlemcen, Fac Sci, Dept Math, BP 119, Tilimsen 13000, Algeria

[3] Univ Mascara, LPQ3M, Mascara 29000, Algeria

关键词: Orthogonal polynomials;    Generating functions;    Recurrence relations;    Ultraspherical polynomials;    Chebyshev polynomials;    Hermite polynomials;   

DOI  :  10.1016/j.jmaa.2016.11.053

来源: Elsevier

【 摘 要 】

We show that the only polynomial sets with a generating function of the form F(xt - R(t)) and satisfying a three -term recursion relation are the monomial set and the rescaled ultraspherical, Hermite, and Chebyshev polynomials of the first kind. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free