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Euler-Mellin integrals and \(A\)-hypergeometric functions. (English) Zbl 1290.32008
Summary: 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.

32A60 Zero sets of holomorphic functions of several complex variables
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
Full Text: DOI Euclid arXiv
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