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

• Autorzy: Stawiska M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

integrals of rational functions; Vandermonde determinant; differential fields; Liouville theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 2
• Strony: 155--159
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Stawiska M.

• Department of Mathematics, University of Kansas 1460 Jayhawk Blvd., Lawrence, KS 66045, USA,

Bibliografia

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• [LS] S. Łojasiewicz, J. Stasica, Analiza formalna i funkcje analityczne, Wydawnictwo Uniwersytetu Jagiellonskiego, Kraków, 2005 [Polish]
• [Ma] I. G. Macdonald, Symmetric functions and Hall polynomials. Second edition. With contributions by A. Zelevinsky. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995.
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• [Ri] R. H. Risch, The problem of integration in finite terms, Trans. Amer. Math. Soc. 139 (1969), 167-189
• [VS] G. D. Villa Salvador, Topics in the theory of algebraic function fields. Mathematics: Theory & Applications. Birkh¨auser Boston, Inc., Boston, MA, 2006.
• [Tr] B. Trager, Algebraic factoring and rational function integration, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, manuscript