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A general investigation of integration in finite form of differential equations of the first order article 1

Published: 01 May 1981 Publication History

Abstract

Numerous investigations on integration in finite form of Abelian integrals are based on theorems of Liouville [6,7,8] and Abel [1].

References

[1]
Abel, Précis d'une théorie des fonctions elliptiques. J. de Crelle 4 (1829).
[2]
Fuchs, Sitzungber. der Berliner Akademie (1884), p. 1171.
[3]
Königsberger. Uber die Reduction Abelscher Integrale aut niedere integralformen speciell auf elliptische integrale, J. de Crelle, 89 (1880), p. 89.
[4]
Königsberger, Allgemeine Untersuchungen aus der Theorie der Differentialgleichungen, Leipzig, 1888 (and several papers in J. de Crelle).
[5]
A. N. Korkin, "Studies on {integrating} factors of differential equations of first order", Moscow Math. Cbornik, 24, 2 (1904), p. 194.
[6]
Liouville, Intégrals dont la valeur est algébrigue. J. de Crelle, 10 (1833), p. 342.
[7]
Liouville, Sur la détermination des integrals dont la valeur est algébrique. J. Ecole Polytechnique 14. Ch 22 (1833), p. 124.
[8]
Liouville, Mémoire sur 1'integration d'une classe des fonctions trancendantes. J. de Crelle, 13 (1835).
[9]
Liouville, Mémoire sur la classification des transcentantes, etc. J. de Liouville 2(1837), p. 56.
[10]
Mordukhai-Boltovskoi, On reduction of Abelian integrals to lower transcendentals, Notices Warsaw Poly. Inst., Part 1, Ch 1, paragraphs 15 to 23 (1905).

Cited By

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  • (2022)Comments on Rosenlicht’s Integration in Finite TermsIntegration in Finite Terms: Fundamental Sources10.1007/978-3-030-98767-1_2(11-30)Online publication date: 7-Jun-2022

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Published In

cover image ACM SIGSAM Bulletin
ACM SIGSAM Bulletin  Volume 15, Issue 2
May 1981
27 pages
ISSN:0163-5824
DOI:10.1145/1089257
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 1981
Published in SIGSAM Volume 15, Issue 2

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  • (2022)Comments on Rosenlicht’s Integration in Finite TermsIntegration in Finite Terms: Fundamental Sources10.1007/978-3-030-98767-1_2(11-30)Online publication date: 7-Jun-2022

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