Abstract
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.
Original language | English (US) |
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Pages (from-to) | 101-123 |
Number of pages | 23 |
Journal | Michigan Mathematical Journal |
Volume | 63 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2014 |