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Groups, conics and recurrence relations

Published online by Cambridge University Press:  03 July 2023

A. F. Beardon
A. F. Beardon*
Affiliation:
D.P.M.M.S., University of Cambridge, Wilberforce Road, Cambridge CB3 0WB e-mail: afb@dpmms.cam.ac.uk

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In this paper we explore some of the geometry that lies behind the real linear, second order, constant coefficient, recurrence relation(1)where a and b are real numbers. Readers will be familiar with the standard method of solving this relation, and, to avoid trivial cases, we shall assume that ab ≠ 0. The auxiliary equation of t2 = at + b of (1) has two (possibly complex) solutionsand the most general solution of (1) is given by

  1. (i) when are real and distinct;

  2. (ii) when

  3. (iii)

.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 569 , July 2023, pp. 193 - 203
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Copyright
© The Authors, 2023. Published by Cambridge University Press on behalf of The Mathematical Association

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