Séminaire du 4 octobre 2010, 14h00: Shaoshi Chen, Équipe-projet Algorithms, INRIA Paris-Rocquencourt.
On the Structure of Hyperexponential-Hypergeometric Functions and the Termination of Creative Telescoping
The method of creative telescoping, first introduced by Zeilberger in the 1990's,
plays an important role in the study of special functions. In particular,
it is applicable to the verification of a large class of identities that
involve integrals or sums of proper hyperexponential-hypergeometric functions.
In this talk, I shall present a structure theorem for multivariate
hyperexponential-hypergeometric functions that generalizes both Abramov and
Petkovsek's result for multivariate hypergeometric terms and the recent
result by Feng, Singer, and Wu for bivariate hyperexponential-hypergeometric
functions. As an application of this structure theorem, I shall then present two
criteria for the existence of telescopers for bivariate hyperexponential-hypergeometric
functions: one for telescopers with respect to the continuous variable,
the other for telescopers with respect to the discrete one. Those criteria
decide the termination of Zeilberger's algorithm in the bivariate continuous-discrete setting.
Work in progress with F. Chyzak, R. Feng, and Z. Li.
Last modified: Mon Sep 20 14:48:07 CEST 2010