FoCM 2014 conference

Workshop C5 - Special Functions and Orthogonal Polynomials

December 18, 17:00 ~ 17:30 - Room A21

## Orthogonal polynomials and integral transforms

### Ana F. Loureiro

### University of Kent, U.K. - A.Loureiro@kent.ac.uk

In this talk I will explain how operating with certain integral transforms over polynomial sequences is a useful tool to obtain and deduce properties of one sequence based on the other. A special attention will be given to certain $d$-orthogonal polynomial sequences, which basically are polynomial sequences satisfying a recurrence relation of order $d+1$. When $d=1$, we recover the orthogonal case. Examples of some known polynomial sequences with a plank of applications will be used to illustrate the usefulness of the technique. Among the targeted sequences, some semiclassical polynomials will arise.