Discrete Geometry Seminar: Hankel Transforms of Orthogonal Polynomials via Riordan Arrays

Event Date: 

Wednesday, February 12, 2014 -
2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Michael Dougherty

Email: dougherty@math.ucsb.edu

Speaker: Michael Dougherty

Abstract: The Hankel transform is a complicated map between integer sequences using large determinants of matrices. Perhaps surprisingly, it produces several elegant results when applied to certain families of sequences. This has led to the application of the Hankel transform to sequences of orthogonal polynomials, and Riordan arrays provide the necessary machinery to understand the result.

In this talk, we will discuss the interplay between these tools and give a (rather nice!) formula for the specific case of the Legendre polynomials. No background in any of the above is needed.