DOI QR코드

DOI QR Code

A GENERALIZATION OF LIOUVILLE′S THEOREM ON INTEGRATION IN FINITE TERMS

  • 발행 : 2002.01.01

초록

A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the $\varepsilon$L-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

키워드

참고문헌

  1. S. Lang, Algebra, Addison-Wesley, Reading, M. A., 1965
  2. D. D. Mordukhai-Boltovskoi, Researches on the integration in finite terms of differential equations of the first order, Communications de la societe mathematique de Kharkov. 10 (1906), 34-64, 231-269
  3. A. Ostrowski, Sur L' integrabilite elemeniaire de quelque classes d' expression, Comm. Math. Helv. 18 (1946), 283-308 https://doi.org/10.1007/BF02568114
  4. J. F. Ritt, Integration in finite terms: Liouville's theory of elementary methods, New York, Columbia University Press, 1948
  5. M. Rosenlicht, Integration in finite terms, Amer. Math. Monthly 79 (1972), 963-972 https://doi.org/10.2307/2318066
  6. M. Rosenlicht, Liouville's theorem on functions with elementary integrals, Pacific J. Math. 24 (1968), 153-161 https://doi.org/10.2140/pjm.1968.24.153
  7. M. Rosenlicht, On Liouville's theory of elementary functions, Pacific J. Math. 65 (1976), 485-492 https://doi.org/10.2140/pjm.1976.65.485
  8. M. F. Singer, B. D. Saunders, and B. F. Caviness, An extension of Liouville's theorem on integration in finite terms, SIAM J. Comput. 14 (1985), 966-990 https://doi.org/10.1137/0214069