Euler--Mellin integrals and A-hypergeometric functions

Details Euler--Mellin integrals and A-hypergeometric functions Euler--Mellin integrals and A-hypergeometric functions

2011-03-31

arxiv.org/abs/1103.6273v1

Mathematics

Complex Variables

13 pages, 2 figures

Scientific paper

We provide a meromorphic continuation of integrals that generalize the Mellin transform of a rational function 1/f and classical Euler integrals. This is naturally related to the coamoeba, and the components of the complement of the closed coamoeba give rise to a family of these so-called Euler--Mellin integrals. We then apply the dependence of these integrals on the coefficients of (the factors of) f to the theory of A-hypergeometric functions.

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