Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields
Commentationes Mathematicae, Tome 50 (2010) no. 2.

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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 coefficients of this series following from the generalized Vandermonde determinant expansion. Our result can be viewed as a parametric version of a classical theorem of Liouville. We also give some applications.
Mots-clés : integrals of rational functions, Vandermonde determinant, differential fields, Liouville theorem 
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     title = {Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields},
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Małgorzata Stawiska. Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields. Commentationes Mathematicae, Tome 50 (2010) no. 2. https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_291812/