Higher order hypergeometric Lauricella function and zero asymptotics of orthogonal polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Martinez-Gonzalez, P.²  Zarzo, A.^1,3 

[1] Univ Politecn Madrid, ETS Ingn Ind, Dept Matemat Aplicada, E-28006 Madrid, Spain

[2] Univ Almeria, Dept Estadist & Matemat Aplicada, E-04120 La Canada De San Urbano, Almeria, Spain

[3] Univ Granada, Fac Ciencias, Inst Carlos Fis Teor & Computac 1, E-18071 Granada, Spain

关键词: Lauricella function;    Orthogonal polynomials;    Zeros;    Asymptotics;   

DOI  :  10.1016/j.cam.2009.02.088

来源: Elsevier

【 摘 要 】

The asymptotic contracted measure of zeros of a large class of orthogonal polynomials is explicitly given in the form of a Lauricella function. The polynomials are defined by means of a three-term recurrence relation whose coefficients may be unbounded but vary regularly and have a different behaviour for even and odd indices. Subclasses of systems of orthogonal polynomials having their contracted measure of zeros of regular, uniform, Wigner, Weyl, Karamata and hypergeometric types are explicitly identified. Some illustrative examples are given. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free