Incomplete A-Hypergeometric Systems

TL;DR

This paper extends the theory of A-hypergeometric systems to include incomplete functions, specifically analyzing an incomplete Gauss hypergeometric function, bridging a gap in the mathematical framework of hypergeometric functions.

Contribution

It generalizes the A-hypergeometric system framework to accommodate incomplete functions, providing new theoretical insights and detailed analysis of an incomplete Gauss hypergeometric function.

Findings

Generalized A-hypergeometric systems for incomplete functions

Detailed study of an incomplete Gauss hypergeometric function

Bridged the gap between hypergeometric theory and incomplete integrals

Abstract

The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta function cannot be understood in this scheme; in other words, the domain of the integration is not cycle (incomplete). We will generalize the theory of A-hypergeometric systems for incomplete functions. We give a general study as well as a detailed study on an incomplete Gauss hypergeometric function.