Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Friday, May, 31, 2013, at University of Waterloo
On the Integrability and Summability of Bivariate Rational Functions
Shaoshi Chen, Department of Mathematics, North Carolina State University

Abstract: Hermite reduction decides whether a univariate rational function has a rational indefinite integral. The discrete analogue of Hermite reduction is Abramov's algorithm. In this talk, we study the rational integrability and summability problem for bivariate rational functions. First, we recall a classical result by Picard in 1902 for testing rational integrability of bivariate rational functions and its application in creative telescoping. Second, we present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions. (Joint work with Manuel Kauers and Michael F. Singer)


Last modified on Thursday, 23 May 2013, at 13:42 hours.