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Funktsional'nyi Analiz i ego Prilozheniya, 2015, Volume 49, Issue 1, Pages 62–70
DOI: https://doi.org/10.4213/faa3170 (Mi faa3170) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
Full-text PDF (172 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa3170
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
Received: 30.04.2013
English version:
Functional Analysis and Its Applications, 2015, Volume 49, Issue 1, Pages 50–56
DOI: https://doi.org/10.1007/s10688-015-0082-3
Bibliographic databases:
Document Type: Article
UDC: 517.312+512.772
Language: Russian
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
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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