Complementary Romanovski–Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions
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In a recent paper (Martínez-Finkelshtein et al. in Proc Am Math Soc 147:2625–2640, 2019) some interesting results were obtained concerning complementary Romanovski–Routh polynomials, a class of orthogonal polynomials on the unit circle and extended regular Coulomb wave functions. The class of orthogonal polynomials here are generalization of the class of circular Jacobi polynomials. In the present paper, in addition to looking at some further properties of the complementary Romanovski–Routh polynomials and associated orthogonal polynomials on the unit circle, behaviour of the zeros of these extended Coulomb wave functions are also studied.
KeywordsRomanovski–Routh polynomials second order differential equations orthogonal polynomials on the unit circle para-orthogonal polynomials
Mathematics Subject Classification42C05 33C47
The colaboration of A. Martínez-Finkelshtein was partially supported by the Spanish government together with the European Regional Development Fund (ERDF) under Grant MTM2017-89941-P (from MINECO), by Junta de Andalucía (the research group FQM-229), and by Campus de Excelencia Internacional del Mar (CEIMAR) of the University of Almería. The author L.L. Silva Ribeiro was supported by the Grant 2017/04358-8 from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) of Brazil. The work of A. Sri Ranga was supported by the Grants 2016/09906-0 of Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and 304087/2018-1 of Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) of Brazil. The author M. Tyaglov was partially supported by The Program for Professor of Special Appointment (Oriental Scholar) at Shanghai Institutions of Higher Learning, by the Joint NSFC-ISF Research Program, jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation (No.11561141001), and by National Natural Science Foundation of China under Grant No. 11871336.
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