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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Functions satisfying elementary relations

Author: Michael F. Singer
Journal: Trans. Amer. Math. Soc. 227 (1977), 185-206
MSC: Primary 12H05
MathSciNet review: 0568865
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Abstract: In this paper we deal with the following problems: When do the solutions of a collection of differential equations satisfy an elementary relation, that is, when is there an equation of the form $ R = 0$ where R is some algebraic combination of logarithmic, exponential and algebraic functions involving solutions of our differential equations? If such relations exist, what can they look like? These problems are given an algebraic setting and general forms for such relations are exhibited. With these, we are able to show that certain classes of functions satisfy no elementary relations.

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Article copyright: © Copyright 1977 American Mathematical Society