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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS

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Author(s):
Dimitrov, Dimitar K. [1] ; dos Santos, Eliel J. C. [2]
Total Authors: 2
Affiliation:
[1] Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 144, n. 2, p. 535-545, FEB 2016.
Web of Science Citations: 1
Abstract

We obtain the explicit form of the expansion of the Jacobi polynomial P-n((alpha, beta)) (1 - 2x/beta) in terms of the negative powers of beta. It is known that the constant term in the expansion coincides with the Laguerre polynomial L-n((alpha))(x). Therefore, the result in the present paper provides the higher terms of the asymptotic expansion as beta -> infinity. The corresponding asymptotic relation between the zeros of Jacobi and Laguerre polynomials is also derived. (AU)

FAPESP's process: 09/13832-9 - Orthogonal polynomials, special functions and applications
Grantee:Dimitar Kolev Dimitrov
Support Opportunities: Research Projects - Thematic Grants