Geodesic
On Algebraic Functions Integrable in Finite Terms
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 62-70

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {A. G. Khovanskii},
     title = {On {Algebraic} {Functions} {Integrable} in {Finite} {Terms}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a4/}
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A. G. Khovanskii. On Algebraic Functions Integrable in Finite Terms. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 62-70. http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a4/