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Supplement to a Note on Recurrent Sequences

Published online by Cambridge University Press:  20 January 2009

C. E. Walsh
C. E. Walsh
Affiliation:
Dublin
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A lemma used in the above paper can be extended to cover the case of a sequence Sn determined by a recurrence relation of the form

r being any positive integer.

For convenience denote everywhere. Let us suppose that an inequality of the form

holds for p = 2, 3, … ., n — 1. The constant K can be determined from the initial values of Sn, when kn and ln have been found.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 3 , February 1933 , pp. 220 - 222
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

page 220 note 1 Proc. Edinburgh Math. Soc. (2), 3 (1932), 147–150.CrossRefGoogle Scholar

page 221 note 1 Bromwich, , Infinite Series (1926), 413.Google Scholar