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

Martínez-Finkelshtein, A.; Silva Ribeiro, L. L. [UNESP]; Sri Ranga, A. [UNESP]; Tyaglov, M.

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

Data

2019-01-01

Autores

Martínez-Finkelshtein, A.

Silva Ribeiro, L. L.

Sri Ranga, A.

Tyaglov, M.

Tipo

Artigo

Direito de acesso

Acesso aberto

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 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.