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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BUS8-0012-0006

Czasopismo

Commentationes Mathematicae

Tytuł artykułu

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

Autorzy Stawiska, M. 
Treść / Zawartość http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/ http://www.staff.amu.edu.pl/~commath/
Warianty tytułu
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, stawiska@ku.edu
Bibliografia
[Co] E. F. Cornelius, Jr., Identities for complete homogeneous symmetric polynomials, preprint, 2009, available at: http://www.scribd.com/doc/16010484/Identities-for-Complete-Homogeneous-Symmetric-Polynomials
[GS] E. A. Gavosto, M. Stawiska, Parabolic explosions in families of complex polynomials, preprint, 2010, to appear in: Essays in Mathematics and its Applications, Dedicated to the 80th Anniversary of Stephen Smale. Edited by P. Pardalos and T. Rassias.
[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.
[Ne] T. Needham, Visual complex analysis, The Clarendon Press, Oxford University Press, New York, 1997
[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
Kolekcja BazTech
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