A central goal of this mathematical research is the use of newly developed relationships between special functions applied to the evaluation of complex integrals. The primary focus is that of the famous Selberg formula for the integration of symmetric functions multiplied against the Vandermonde determinant, acting as a weight. Work will continue addressing possible extensions of this closed form expression. Initial efforts will be made to establish a formula for the ratios of alternantes to the Selberg symmetric functions. It is expected that they will be given explicitly in terms of tournaments. Work will also be done on beta type distributions and their orthogonal polynomials. In addition, the classification of functions which provide extensions of the q- Dyson theorem of Zeilberger and Bressoud will be sought. It is conjectured that not all such functions will turn out to be symmetric.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9002043
Program Officer
John V. Ryff
Project Start
Project End
Budget Start
1990-07-01
Budget End
1992-12-31
Support Year
Fiscal Year
1990
Total Cost
$40,418
Indirect Cost
Name
Arizona State University
Department
Type
DUNS #
City
Tempe
State
AZ
Country
United States
Zip Code
85281