Euler--Mellin integrals and A-hypergeometric functions
Complex Variables
2013-02-04 v2
Abstract
We consider integrals that generalize both the Mellin transforms of rational functions of the form 1/f and the classical Euler integrals. The domains of integration of our so-called Euler--Mellin integrals are naturally related to the coamoeba of f, and the components of the complement of the closure of the coamoeba give rise to a family of these integrals. After performing an explicit meromorphic continuation of Euler--Mellin integrals, we interpret them as A-hypergeometric functions and discuss their linear independence and relation to Mellin--Barnes integrals.
Cite
@article{arxiv.1103.6273,
title = {Euler--Mellin integrals and A-hypergeometric functions},
author = {Christine Berkesch and Jens Forsgård and Mikael Passare},
journal= {arXiv preprint arXiv:1103.6273},
year = {2013}
}
Comments
19 pages, 3 figures; Contains additional results on linear independence and relation to Mellin--Barnes integrals of Euler--Mellin integrals; Introduction revised