Solutions of a class of nonlinear recursive equations and applications

Charinthip Hengkrawit^a, Vichian Laohakosol^b,c, Watcharapon Pimsert^b,*

ABSTRACT: A class of recursive equations extending those of the form y_n=(y_n−2y_n−1−1)/(y_n−2+y_n−1) is transformed into a special case of the nonlinear recursive equation x_n=cx_n−1^h₁(n)x_n−2^h₂(n)...x_n−l+1^h_l−1(n)x_n−l^h_l(n). A general solution of this equation is determined by solving its associated linear difference equation. Several known results are derived as special cases. Connections of the case l=2 to continued fractions are elaborated.

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^a	Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
^b	Department of Mathematics, Institute for Advanced Studies, Kasetsart University, Bangkok 10900, Thailand
^c	Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

* Corresponding author, E-mail: charinthip@mathstat.sci.tu.ac.th

Received 29 Aug 2010, Accepted 12 Apr 2011

Solutions of a class of nonlinear recursive equations and applications

Charinthip Hengkrawita, Vichian Laohakosolb,c, Watcharapon Pimsertb,*

Charinthip Hengkrawit^a, Vichian Laohakosol^b,c, Watcharapon Pimsert^b,*