Polynomials obtained from a recurrence relation which is a modification of the recurrence relation satisfied by orthogonal polynomials

• Grant number: 18/00396-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2018
• End date: December 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Nguyen Thi Hoang Yen
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 16/09906-0 - Harmonic analysis, approximation theory and applications, AP.TEM

Abstract

This project is about preparing the candidate to have the necessary knowledge to be able to undertake research in areas of Orthogonal Polynomials and Special Functions, in particular regarding orthogonal polynomials on the unit circle. As the candidate will be in her second year of graduation in mathematics, the first nine months of the project will be dedicated to obtain basic information about the theory and applications of orthogonal polynomials on the real line. During the last three months of the project, she will study the properties of the polynomials generated by a special recurrence relation, different from that satisfied by orthogonal polynomials on the real line. Recent observations show that, special cases of these polynomials have interesting connections to some special functions, such as, for example, the Bessel functions. (AU)