Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields

Details Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields

2010-04-29

arxiv.org/abs/1004.5536v1

Commentationes Mathematicae, vol. 50, no.2, (2010), 155-159

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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