Three Recitations on Holonomic Systems and Hypergeometric Series

A tutorial on what later became to be known as WZ theory, as well as a motivated account of the seminal Gosper algorithm.Comment: Plain Te

Identities in search of identity

AbstractThe time is ripe to start a science of identities for their own sake, without paying lip-service to high-brow mathematics. Although putting combinatorial, (abstract-)algebraic or analytic flesh and blood on identities did lead and will lead to considerable insight as well as new identities, there is also much to be gained in forgetting advanced mathematics, and starting a new sub-discipline of high-school mathematics called the theory of identities.Preamble. I would like to add to Xavier Viennot's charming after-dinner speech, in which he listed a large set of properties that conferences may have, and which were all enjoyed by the present one, in addition to ”something special that comes from the heart“, the following. There are many conferences in which a Bourbaki is an invited speaker, and many conferences in which a software developer is an invited speaker, but this one is the first one, that I know of, that has both (Pierre Cartier and Gaston Gonnet, respectively.) So we are nearing the blissful days of the mathematical messiah in which Concrete shall dwell with Abstract

Advanced Determinant Calculus: A Complement

This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441-456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.Comment: AmS-LaTeX, 85 pages; Final, largely revised versio