Orthogonal Polynomials and q-Series

Description

We explore several ideas involving orthogonal polynomials and orthogonal functions. We identify new functions and polynomials that have many interesting properties. These functions have the potential to appear in applied problems. We plan to study these functions in detail. Another problem is to determine the behavior of standard polynomials (of the Askey Scheme) when the degree tends to infinity and we also consider the case when a degree dependent parameter depends on the degree. We also intend to identify isochronous systems using our newly discovered biorthogonal rational functions. We also intend to use new ideas to classify combinatorial identities using the so called Rodrigues type formulas.