Analytic Complexity of Hypergeometric Functions Satisfying Systems with Holonomic Rank Two
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.
KeywordsHypergeometric systems of partial differential equations Holonomic rank Analytic complexity Differential polynomial Hypergeometry package
This research was performed in the framework of the basic part of the scientific research state task in the field of scientific activity of the Ministry of Education and Science of the Russian Federation, project “Intellectual analysis of big textual data in finance, business, and education by means of adaptive semantic models”, grant No. 2.9577.2017/8.9.