Complementary Romanovski-Routh polynomials and functions with hybrid orthogonality

Author(s)

Luana de Lima Silva Ribeiro

• Document type: Doctoral Thesis
• Press: São José do Rio Preto. 2019-03-14.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2019-03-01
• Advisor: Alagacone Sri Ranga

Abstract

We consider properties and applications of the complementary Romanovski-Routh polynomials and functions defined in [−1, 1] that satisfy a hybrid orthogonality. These functions are related with a class of para-orthogonal polynomials in the unit circle through the Cayley transform and through Delsarte and Genin transform, respectively. The complementary Romanovski-Routh polynomials are related to the regular Coulomb wave functions and also to the regular Bessel functions. Furthermore, their zeros coincide with the coordinates of the equilibrium point of an energy function. We also explore the expansion of functions in series of functions of hybrid orthogonality and results concerning convergence and Bessel-type inequality were obtained. Moreover, this expansion is given by a modified least square method. (AU)

• FAPESP's process: 17/04358-8 - Applications of functions satisfying certain recurrence relations
• Grantee: Luana de Lima Silva Ribeiro
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)