Quartics, Log-Concavity and Computer Algebra

Description

Abstract: Victor Moll begins his article "The evaluation of integrals: A personal story" (Notices of the AMS, 2002) with the remark, "... It was even more a surprise to discover that new things can still be said today about the mundane subject of integration of rational functions of a single variable and that this subject has connections with branches of contemporary mathematics as diverse as combinatorics, special functions, elliptic curves, and dynamical systems." In this talk I will add another ingredient to his story, namely computer algebra. I will show how recently developed procedures can be used to retrieve observations which in Moll's original approach were derived with classical methods, like the positivity of the coefficients of a specialized family of Jacobi polynomials. In addition, as a result from a recent cooperation with Manuel Kauers (RISC), I will demonstrate that computer algebra can do even more, namely by proving Moll's longstanding log-concavity conjecture with a combination of various algorithms. These applications will lead to a variety of questions in connection with the general theme of the Dagstuhl Seminar ("Challenges in Symbolic Computation Software"

Period	02 Jul 2006
Event title	Dagstuhl Seminar No. 06271. Invited talk at Challenges in Symbolic Computation Software
Event type	Other
Location	GermanyShow on map