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Journal of the London Mathematical Society 2002 66(2):377-387; doi:10.1112/S0024610702003423
© 2002 by London Mathematical Society
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© The London Mathematical Society

An Entire Function Defined by a Nonlinear Recurrence Relation

A. N. W. Hone, N. Joshi and A. V. Kitaev

Department of Pure Mathematics, University of Adelaide Adelaide 5005, Australia

Received 22 January 2001. Revision received 19 September 2001.

For the nonlinear recurrence relation


Formula

it is proved that the limit


Formula

exists and defines an entire function of {alpha}2 = {alpha}1(1-{alpha}1).

Institute of Mathematics and Statistics, University of Kent, Canterbury, Kent CT2 7NF, anwh{at}ukc.ac.uk

School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia, nalini{at}maths.usyd.edu.au

Steklov Mathematical Institute, Fontanka 27, 191011 Russia, kitaev{at}pdmi.ras.ru


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