Euler-Mellin Integrals and A-Hypergeometric Functions

• 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.

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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