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Linear Differential Equations and the Oscillatory Property of Maclaurin's Cosine Series

Published online by Cambridge University Press:  03 November 2016

Aurel Wintner
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Extract

It is well known that, if.

cos t>Cn(t) or cos t<Cn(t) holds for 0< t< ∞ according as n = 1, 3, 5, … or n = 2, 4, 6, …. It will be noted that this is not obvious in itself. In fact, the absolute values of the successive terms of the alternating series do not decrease from m = 0 onward, except when t is small.

Type
Research Article
Information
The Mathematical Gazette , Volume 33 , Issue 303 , February 1949 , pp. 26 - 28
Copyright
Copyright © The Mathematical Association 1949

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