Неэлементарность некоторых интегралов элементарных функций
Matematicheskoe Prosveshchenie, Matematicheskoe Prosveshchenie (2003), pp. 126-135.

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

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     author = {V. V. Prasolov},
     title = {{\CYRN}{\cyre}{\cyrerev}{\cyrl}{\cyre}{\cyrm}{\cyre}{\cyrn}{\cyrt}{\cyra}{\cyrr}{\cyrn}{\cyro}{\cyrs}{\cyrt}{\cyrsftsn} {\cyrn}{\cyre}{\cyrk}{\cyro}{\cyrt}{\cyro}{\cyrr}{\cyrery}{\cyrh} {\cyri}{\cyrn}{\cyrt}{\cyre}{\cyrg}{\cyrr}{\cyra}{\cyrl}{\cyro}{\cyrv} {\cyrerev}{\cyrl}{\cyre}{\cyrm}{\cyre}{\cyrn}{\cyrt}{\cyra}{\cyrr}{\cyrn}{\cyrery}{\cyrh} {\cyrf}{\cyru}{\cyrn}{\cyrk}{\cyrc}{\cyri}{\cyrishrt}},
     journal = {Matematicheskoe Prosveshchenie},
     pages = {126--135},
     publisher = {mathdoc},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MP_2003_a10/}
}
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V. V. Prasolov. Неэлементарность некоторых интегралов элементарных функций. Matematicheskoe Prosveshchenie, Matematicheskoe Prosveshchenie (2003), pp. 126-135. http://geodesic.mathdoc.fr/item/MP_2003_a10/

[1] Devenport Dzh., Integrirovanie algebraicheskikh funktsii, Mir, M., 1985

[2] Kaplanskii I., Vvedenie v differentsialnuyu algebru, IL, M., 1959

[3] Kolchin E. R., Differential algebra and algebraic groups, Academic Press, London, 1973 | MR | Zbl

[4] Liouville J., “Sur la detérmination des integrales dont la valeur est algébrique”, J. École Polytech., 14 (1833), 124–193

[5] Magid A. R., Lectures on differential Galois theory, University Lecture Series, 7, AMS, Providence, RI, 1994 | MR | Zbl

[6] Rosenlicht M., “Liouville's theorem for functions with elementary integrals”, Pacific J. Math., 24 (1968), 153–161 | MR | Zbl

[7] Rosenlicht M., “Integration in finite terms”, Amer. Math. Monthly, 79 (1972), 963–972 | DOI | MR | Zbl