Dagstuhl Seminar No. 06271. Invited talk at Challenges in Symbolic Computation Software
Sprache des Tagungstitel:
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"