Incomplete Hypergeometric Systems Associated to 1-Simplex $\times$ (n-1)-Simplex

TL;DR

This paper explores an incomplete analog of the well-studied A-hypergeometric systems associated with 1-simplex times (n-1)-simplex, aiming to extend understanding of these special functions.

Contribution

It introduces and investigates an incomplete version of the A-hypergeometric systems related to 1-simplex and (n-1)-simplex, expanding the class of known hypergeometric functions.

Findings

Characterization of the incomplete hypergeometric systems.

Identification of properties distinguishing them from complete systems.

Potential applications in related mathematical fields.

Abstract

The A-hypergeometric system was introduced by Gel'fand, Kapranov and Zelevinsky in the 1980's. Among several classes of A-hypergeometric functions, those for 1-simplex $\times$ (n-1)-simplex are known to be a very nice class. We will study an incomplete analog of this class.