Complementary romanovski-routh polynomials: From orthogonal polynomials on the unit circle to coulomb wave functions

• Autor(a) principal: Martínez-Finkelshtein, A.
• Data de Publicação: 2019
• Outros Autores: Silva Ribeiro, L. L. [UNESP], Sri Ranga, A. [UNESP], Tyaglov, M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1090/proc/14423; http://hdl.handle.net/11449/189097
• topic: Coulomb wave functions; Para-orthogonal polynomials on the unit circle; RomanovsKi-Routh polynomials; Second order differential equations

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 Schrödinger 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.