Non-Gaussian integrals and general hypergeometric functions

TL;DR

This paper develops a comprehensive theory for non-Gaussian integrals, which involve arbitrary functions multiplied by exponential polynomials, extending and simplifying the existing framework of hypergeometric functions.

Contribution

It introduces a generalized theory of non-Gaussian integrals that broadens and streamlines the understanding of hypergeometric functions as defined by Gelfand et al.

Findings

Unified framework for non-Gaussian integrals

Simplified approach to hypergeometric functions

Potential applications in mathematical physics

Abstract

By a non-Gaussian integral we mean integral of the product of an arbitrary function and exponent of a polynomial. We develop a theory of such integrals, which generalizes and simplifies the theory of general hypergeometric functions in the sense of I. M. Gelfand et al.