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On algebraic functions integrable in finite terms

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Functional Analysis and Its Applications Aims and scope

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.

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Authors and Affiliations

  1. Institute for System Analysis, Russian Academy of Sciences, St.-Petersburg, Russia

    A. G. Khovanskii

  2. Independent University of Moscow, Moscow, Russia

    A. G. Khovanskii

  3. The University of Toronto, Toronto, Canada

    A. G. Khovanskii

Authors
  1. A. G. Khovanskii
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Correspondence to A. G. Khovanskii.

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To the memory of Vladimir Igorevich Arnold

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 1, pp. 62–70, 2015

Original Russian Text Copyright © by A. G. Khovanskii

This work was supported in part by Canadian Grant no. 0GP0156833.

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Khovanskii, A.G. On algebraic functions integrable in finite terms. Funct Anal Its Appl 49, 50–56 (2015). https://doi.org/10.1007/s10688-015-0082-3

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  • DOI: https://doi.org/10.1007/s10688-015-0082-3

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