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Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields (1004.5536v1)
Published 29 Apr 2010 in math.CA
Abstract: We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients following from generalized Vandermonde determinant expansion. Our result can be viewed as a parametric version of a classical theorem of Liouville. We also give applications.