# WZ Cohomology

## ABSTRACT

In a series of seminal papers, Wilf and Zeilberger (herewith WZ) have established an impeccable bases in the field of Algorithmic Proof Theory. In particular the traditional savoir-faire of proving single and multi-variable special functions, even holonomic, identities is now made automatic.

The present talk aims at exploiting further application of the theory, in a different direction. To wit: a conceptual framework of the WZ methodology will be tied together with discrete-continuous difference- differential forms

\Omega= \sum_{|I|=r}f_I \delta m_I + \sum_{|J|=s}g_J dx_J,

as well as winged to systematized Apéry-style irrationality proofs (once regarded as a tour-de-force in Number Theory); hypergeometric and q-hypergeometric series accelerations and constructions of an infinite string of WZ-forms will be given.

The notion of a WZ Cohomology and its computation will be shown as seated at the heart of the matter.

(joint work with D. Zeilberger)

Speaker's Contact Info: tewodros(at-sign)euclid.math.temple.edu