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2011

Euler--Mellin integrals and A-hypergeometric functions

Berkesch, Christine, Forsgård, Jens, Passare, Mikael

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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.

Euler--Mellin integrals and A-hypergeometric functions · Around

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Eduardo Cattani, Carlos D’Andrea, and Alicia Dickenstein, The A A -hypergeometric system associated with a monomial curve, Duke Math. J
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