Date: Monday, March 21, 2005 Time: 4:00 p.m. Room: Little Hall (LIT) 109 Opening Remarks by George E. Andrews Evan Pugh Professor of Mathematics The Pennsylvania State University Refreshments: 5:00 p.m. in LIT 339

Abstract: Orthogonal polynomials seemed to have first been developed by Legendre and Laplace in their work on celestial mechanics. One of the next developments was work of Laplace on probability theory. Both of these dealt with specific sets of orthogonal polynomials, first polynomials orthogonal with respect to a symmetric beta distribution on (-1,1) and then the normal distribution on the whole real line. The general theory starts with Chebyshev in the 1850s. A small sample of what is known about specific sets of orthogonal polynomials, the general theory, and some uses will be described. Uses range from partitions to quantum theory of angular momentum. In both of these cases, it was not known until about 25 years ago that orthogonal polynomials were there. In one case the polynomials were known but not the orthogonality. In the other, the orthogonality was know, but ...

 ^* Professor Richard Askey is one of the world's foremost authorities in the field of Special Functions. Over the past several decades he has had a profound influence on that subject through his own research as well as through the work of his several students. Along with George Andrews and Bruce Berndt, he is one of the three greatest experts on the work of the Indian mathematical genius Srinivasa Ramanujan. At the University of Wisconsin he held the Gabor Szego Professorship during 1986-95, and since 1995 he is John Bascom Professor of Mathematics there. He is a Member of the National Academy of Sciences, and is an Honorary Fellow of the Indian Academy of Sciences.

This lecture is part of the Mathematics Department's Special Year in Number Theory and Combinatorics. For more information see the website:
http://www.math.ufl.edu/specialyears/2004-5/