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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.)

COMPLEMENTARY ROMANOVSKI-ROUTH POLYNOMIALS: FROM ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE TO COULOMB WAVE FUNCTIONS

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Author(s):
Martinez-Finkelshtein, A. [1, 2] ; Silva Ribeiro, L. L. [3] ; Sri Ranga, A. [4] ; Tyaglov, M. [5]
Total Authors: 4
Affiliation:
[1] Baylor Univ, Dept Math, Waco, TX 76798 - USA
[2] Univ Almeria, Dept Matemat, Alameria 04120 - Spain
[3] UNESP Univ Estadual Paulista, Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[4] UNESP Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[5] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai - Peoples R China
Total Affiliations: 5
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 147, n. 6, p. 2625-2640, JUN 2019.
Web of Science Citations: 0
Abstract

We consider properties and applications of a sequence of polynomials known as complementary Romanovski-Routh polynomials (CRR polynomials for short). These polynomials, which follow from the Romanovski-Routh polynomials or complexified Jacobi polynomials, are known to be useful objects in the studies of the one-dimensional Schrodinger equation and also the wave functions of quarks. One of the main results of this paper is to show how the CRR-polynomials are related to a special class of orthogonal polynomials on the unit circle. As another main result, we have established their connection to a class of functions which are related to a subfamily of Whittaker functions that includes those associated with the Bessel functions and the regular Coulomb wave functions. An electrostatic interpretation for the zeros of CRR-polynomials is also considered. (AU)

FAPESP's process: 17/12324-6 - Orthogonal polynomials on the unit circle and related studies
Grantee:Alagacone Sri Ranga
Support Opportunities: Regular Research Grants
FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
Grantee:Dimitar Kolev Dimitrov
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 17/04358-8 - Applications of functions satisfying certain recurrence relations
Grantee:Luana de Lima Silva Ribeiro
Support Opportunities: Scholarships in Brazil - Doctorate (Direct)