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

Autor(es)

Martinez-Finkelshtein, A. ^{[1, 2]} ; Silva Ribeiro, L. L. ^[3] ; Sri Ranga, A. ^[4] ; Tyaglov, M. ^[5]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 147, n. 6, p. 2625-2640, JUN 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/12324-6 - Polinômios ortogonais no círculo unitário e estudos relacionados
• Beneficiário: Alagacone Sri Ranga
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/04358-8 - Aplicações de funções que satisfazem certas relações de recorrência
• Beneficiário: Luana de Lima Silva Ribeiro
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto