Cohomology groups for recurrence relations and contiguity relations of hypergeometric systems

Abstract

We develop the theory of cohomology groups for recurrence relations, based upon the asymptotic analysis of finite difference equations carried out in a previous paper. We apply it to compute the Gevrey extension groups of the $\mathcal{D}$-modules associated to some confluent hypergeometric systems. In those applications, recurrence relations appear as contiguity relations of hypergeometric systems.