RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 62–70 (Mi faa3170)  

On Algebraic Functions Integrable in Finite Terms

A. G. Khovanskiiabc

a Institute of Systems Analysis, Russian Academy of Sciences
b Independent University of Moscow
c Department of Mathematics, University of Toronto

Abstract: Liouville's theorem describes algebraic functions integrable in terms of generalized elementary functions. In many cases, algorithms based on this theorem make it possible to either evaluate an integral or prove that the integral cannot be “evaluated in finite terms.” The results of the paper do not improve these algorithms but shed light on the arrangement of the $1$-forms integrable in finite terms among all $1$-forms on an algebraic curve.

Keywords: Abelian integral, algebraic function, elementary function, solvability in finite terms

Funding Agency Grant Number
Canadian Grant 0GP0156833


DOI: https://doi.org/10.4213/faa3170

Full text: PDF file (172 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2015, 49:1, 50–56

Bibliographic databases:

UDC: 517.312+512.772
Received: 30.04.2013

Citation: A. G. Khovanskii, “On Algebraic Functions Integrable in Finite Terms”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 62–70; Funct. Anal. Appl., 49:1 (2015), 50–56

Citation in format AMSBIB
\Bibitem{Kho15}
\by A.~G.~Khovanskii
\paper On Algebraic Functions Integrable in Finite Terms
\jour Funktsional. Anal. i Prilozhen.
\yr 2015
\vol 49
\issue 1
\pages 62--70
\mathnet{http://mi.mathnet.ru/faa3170}
\crossref{https://doi.org/10.4213/faa3170}
\zmath{https://zbmath.org/?q=an:06485785}
\elib{http://elibrary.ru/item.asp?id=23421404}
\transl
\jour Funct. Anal. Appl.
\yr 2015
\vol 49
\issue 1
\pages 50--56
\crossref{https://doi.org/10.1007/s10688-015-0082-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000351307000005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924940272}


Linking options:
  • http://mi.mathnet.ru/eng/faa3170
  • https://doi.org/10.4213/faa3170
  • http://mi.mathnet.ru/eng/faa/v49/i1/p62

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:374
    Full text:89
    References:43
    First page:40

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020