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. https://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 | ||||||
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Additional Information: | Copyright © 1933 by the National Academy of Sciences Communicated September 6, 1933 | ||||||
Issue or Number: | 10 | ||||||
Record Number: | CaltechAUTHORS:WARpnas33 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:WARpnas33 | ||||||
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: | 02 Oct 2019 23:13 |
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