An extension of Liouville's theorem on integration in finite terms

Authors:
M. F. Singer;B. D. Saunders;B. F. Caviness
Affiliations:
-;-;-
Venue:
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Year:
1981

Citing 2
Cited 1

An extension of Liouville's theorem

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The integration of a class of special functions with the Risch algorithm

ACM SIGSAM Bulletin

Integration in finite terms

ACM SIGSAM Bulletin

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Abstract

In this paper we give an extension of the Liouville theorem [RISC69, p. 169] and give a number of examples which show that integration with special functions involves some phenomena that do not occur in integration with the elementary functions alone. Our main result generalizes Liouville's theorem by allowing, in addition to the elementary functions, special functions such as the error function, Fresnel integrals and the logarithmic integral to appear in the integral of an elementary function. The basic conclusion is that these functions, if they appear, appear linearly.