Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Definite Integration Revisited
Speaker: Jacques Carette, McMaster University
Date: Thursday, March 3, 2011 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
The definition of integration has been greatly generalized since Riemann, but in a surprising direction: less and less continuous, even less defined, functions are integrable. On the other hand, perfectly nice functions (holonomic and/or with closed forms) which are analytic outside some (often rather mild) singularities are not integrable. By revisiting the process of (definite) integration, we can define an 'integral' which can cope with (some) singularities, with a quite close parallel to summation strategies for divergent series. We derive new effective algorithms for (classical) definite integration in closed-form from this method. But we also get insights into why such a generalization is qualitatively different than previous generalizations since, like summation of divergent series, the 'integral' is no longer process-independent in the general case.