Talk: When does Almkvist-Zeilberger's algorithms succeed?

Speaker: Shaoshi Chen

Abstract:

We present two criteria for the existence of telescopers for bivariate
hyperexponential-hypergeometric functions. One is for the existence of
telescopers with respect to the continuous variable, the other for
telescopers with respect to the discrete one. Our criteria are based on a standard
representations of  bivariate hyperexponential-hypergeometric functions, and two
additive decompositions.
With those criteria, we determine the termination of Almkvist-Zeilberger's algorithms
for bivariate hyperexponential-hypergeometric inputs.