Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:300

Article

Manas-Manas, Juan F.¹  Marcellan, Francisco^2,3  Moreno-Balcazar, Juan J.^1,4 

[1] Univ Almeria, Dept Matemat, Almeria, Spain

[2] Univ Carlos III Madrid, Inst Ciencias Matemat ICMAT, E-28903 Getafe, Spain

[3] Univ Carlos III Madrid, Dept Matemat, E-28903 Getafe, Spain

[4] Inst Carlos I Fis Teor & Computac, Granada, Spain

关键词: Sobolev orthogonal polynomials;    Jacobi polynomials;    Mehler-Heine formulae;    Asymptotics;    Zeros;   

DOI  :  10.1016/j.cam.2016.01.010

来源: Elsevier

【 摘 要 】

In this contribution we deal with a varying discrete Sobolev inner product involving the Jacobi weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and the behavior of their zeros. We are interested in Mehler-Heine type formulae because they describe the essential differences from the point of view of the asymptotic behavior between these Sobolev orthogonal polynomials and the Jacobi ones. Moreover, this asymptotic behavior provides an approximation of the zeros of the Sobolev polynomials in terms of the zeros of other well-known special functions. We generalize some results appeared in the literature very recently. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free