The problem of integration in finite terms
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- by Robert H. Risch PDF
- Trans. Amer. Math. Soc. 139 (1969), 167-189 Request permission
References
- Martin Davis, Computability and unsolvability, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR 0124208
- Martin Davis, Hilary Putnam, and Julia Robinson, The decision problem for exponential diophantine equations, Ann. of Math. (2) 74 (1961), 425–436. MR 133227, DOI 10.2307/1970289
- Irving Kaplansky, An introduction to differential algebra, Publ. Inst. Math. Univ. Nancago, No. 5, Hermann, Paris, 1957. MR 0093654
- E. R. Kolchin, Galois theory of differential fields, Amer. J. Math. 75 (1953), 753–824. MR 58591, DOI 10.2307/2372550
- Wolfgang Krull, Elementare und klassische Algebra. II, Sammlung Göschen, Bd. 933, Walter de Gruyter & Co., Berlin, 1959 (German). MR 0108481 J. Liouville, Sur la determination des integrales dont la valeur est algébrique, J. École Polytech. 14 (1833), 124-193. —, Mémoire sir les transcendantes elliptiques de premiére et de seconde espéce, considerées comme fonctiones de leur amplitude, J. École Polytech. 14 (1833), 57-83. D. D. Mordoukhay-Boltovskoy, On the integration of transcendental functions, Warsaw Univ. Izv. nos. 6-9 (1913). (Russian)
- A. Ostrowski, Sur l’intégrabilité élémentaire de quelques classes d’expressions, Comment. Math. Helv. 18 (1946), 283–308 (French). MR 16763, DOI 10.1007/BF02568114
- Joseph Fels Ritt, Integration in Finite Terms. Liouville’s Theory of Elementary Methods, Columbia University Press, New York, N. Y., 1948. MR 0024949, DOI 10.7312/ritt91596
- Maxwell Rosenlicht, Liouville’s theorem on functions with elementary integrals, Pacific J. Math. 24 (1968), 153–161. MR 223346, DOI 10.2140/pjm.1968.24.153
- A. Seidenberg, Abstract differential algebra and the analytic case, Proc. Amer. Math. Soc. 9 (1958), 159–164. MR 93655, DOI 10.1090/S0002-9939-1958-0093655-0 D. M. Sintzov, Rational integrals of linear equations, Učen. Zap. Kazan Univ. 65 (1898). (Russian) B. L. van der Waerden, Modern algebra. Vol. I, Ungar, New York, 1949.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 139 (1969), 167-189
- MSC: Primary 12.80
- DOI: https://doi.org/10.1090/S0002-9947-1969-0237477-8
- MathSciNet review: 0237477