Euler-Mellin integrals and A-hypergeometric functions

By C. Berkesch, J. Forsgaard, Mikael Passare. 2011

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We consider integrals that generalize both Mellin transforms of rational functions of the form 1/f and 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 this 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.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b4542ac2b7839e28587cf2f19d23b531c53a2bd2