Analytic Complexity of Hypergeometric Functions Satisfying Systems with Holonomic Rank Two

Abstract

We investigate the analytic complexity of solutions to holonomic bivariate hypergeometric systems of the Horn type by means of a Mathematica package. We classify hypergeometric systems with holonomic rank two by the polygons of the Ore–Sato coefficients up to transformations of the defining matrices which do not affect the analytic complexity of solutions. We establish an upper bound for the analytic complexity of solutions to bivariate hypergeometric systems with holonomic rank two.