B. F. Caviness

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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,(More)
In this paper a generalization of the Risch Structure Theorem is reported. The generalization applies to fields F (t<inf>1</inf>,...,t<inf>n</inf>) where F is a differential field (in our applications F will be a finitely generated extension of Q, the field of rational numbers) and each t<inf>i</inf> is either algebraic over F<inf>i-1</inf> =(More)
It is a well-known empirical result that differentiation, especially higher order differentiation, of simple expressions can lead to long and complex expressions. In this paper we give some theoretical results that help to explain this phenomenon. In particular we show that in certain representations there exist expressions whose representations require(More)
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