Integral of exponent of a polynomial is a generalized hypergeometric function of the coefficients of the polynomial

TL;DR

This paper demonstrates that the integral of the exponential of any polynomial function can be expressed as a solution to a generalized hypergeometric differential system, linking polynomial integrals to special functions.

Contribution

It establishes a connection between polynomial exponential integrals and generalized hypergeometric functions through differential equations.

Findings

Integral satisfies a generalized hypergeometric system

Provides a new perspective on polynomial integrals

Links polynomial exponentials to special functions

Abstract

We show that the integral \int e^{S(x_1,...,x_n)}dx_1...dx_n, for an arbitrary polynomial S, satisfies a generalized hypergeometric system of differential equations in the sense of I. M. Gelfand et al.