Complementary romanovski-routh polynomials: From orthogonal polynomials on the unit circle to coulomb wave functions
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Data
2019-01-01
Autores
Martínez-Finkelshtein, A.
Silva Ribeiro, L. L. [UNESP]
Sri Ranga, A. [UNESP]
Tyaglov, M.
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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.
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Coulomb wave functions, Para-orthogonal polynomials on the unit circle, RomanovsKi-Routh polynomials, Second order differential equations
Como citar
Proceedings of the American Mathematical Society, v. 147, n. 6, p. 2625-2640, 2019.