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A Property of Recurring Series

Ward, Morgan (1933) A Property of Recurring Series. Proceedings of the National Academy of Sciences of the United States of America, 19 (10). pp. 914-916. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:WARpnas33

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Abstract

If (U): U1, U2, ... , Un,.., denotes a sequence of rational numbers satisfying a linear difference equation of order k with rational coefficients, then if a group of k consecutive terms of (U) ever repeats itself, all the roots of the polynomial associated with the difference equation are roots of unity, and the sequence (U) is periodic. [1] I show here that the like occurs, generally speaking, if one term of the sequence repeats itself at regular intervals a sufficient number of times.


Item Type:Article
Additional Information:Copyright © 1933 by the National Academy of Sciences Communicated September 6, 1933
Record Number:CaltechAUTHORS:WARpnas33
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:WARpnas33
Alternative URL:http://www.pnas.org/content/vol19/issue10/
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4482
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:24 Aug 2006
Last Modified:14 Nov 2014 19:19

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