대한수학회지 (Journal of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.13-30
  • /
  • 2002
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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A GENERALIZATION OF LIOUVILLE′S THEOREM ON INTEGRATION IN FINITE TERMS

  • 발행 : 2002.01.01
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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.

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참고문헌

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  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