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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A completeness theorem for trigonometric identities and various results on exponential functions


Author: Lou van den Dries
Journal: Proc. Amer. Math. Soc. 96 (1986), 345-352
MSC: Primary 03B25; Secondary 03C05, 08B05
DOI: https://doi.org/10.1090/S0002-9939-1986-0818470-6
MathSciNet review: 818470
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Abstract: All valid identities in terms of variables, real constants, the arithmetic operations of addition and multiplication, and the trigonometric operations of sine and cosine are shown to be consequences of a few familiar identities and numerical facts. We also indicate how to decide whether $ f$ eventually dominates $ g$, for $ f$ and $ g$ from a certain class of exponential functions. Finally, we correct a statement from an earlier paper.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818470-6
Article copyright: © Copyright 1986 American Mathematical Society