April 2023 MORE SOLUTIONS TO NONLINEAR RECURRENCE EQUATIONS
Christopher S. Withers, Saralees Nadarajah
Rocky Mountain J. Math. 53(2): 579-587 (April 2023). DOI: 10.1216/rmj.2023.53.579

Abstract

Let F(x) be any analytic function. Suppose that w is a fixed point of F(x), that is, F(w)=w. We previously (Rocky Mountain J. Math. 52:6 (2022)) gave solutions of the recurrence equation xn+1=F(xn) for n=0,1,2,. In this note, we give more general solutions of the form

xn=w+i=1Ai(unrn)i

for any un such that unun+11 as n.

Citation

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Christopher S. Withers. Saralees Nadarajah. "MORE SOLUTIONS TO NONLINEAR RECURRENCE EQUATIONS." Rocky Mountain J. Math. 53 (2) 579 - 587, April 2023. https://doi.org/10.1216/rmj.2023.53.579

Information

Received: 23 December 2021; Accepted: 23 May 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604775
zbMATH: 07725156
Digital Object Identifier: 10.1216/rmj.2023.53.579

Subjects:
Primary: 65H20

Keywords: Analytic function , Bell polynomial , recurrence relation

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 2 • April 2023
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