Open AccessComplementary Romanovski-Routh polynomials: From orthogonal polynomials on the unit circle to Coulomb wave functions
Author(s) -
Andrei Martínez–Finkelshtein,
Luana L. Silva Ribeiro,
A. Sri Ranga,
Mikhail Tyaglov
Publication year - 2018
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14423
Subject(s) - orthogonal polynomials , discrete orthogonal polynomials , classical orthogonal polynomials , mathematics , wilson polynomials , difference polynomials , hahn polynomials , gegenbauer polynomials , jacobi polynomials , bessel polynomials , pure mathematics , mathematical analysis
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.
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