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Research articles

ScienceAsia 37 (2011): 136-144 |doi: 10.2306/scienceasia1513-1874.2011.37.136


Solutions of a class of nonlinear recursive equations and applications


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

 
ABSTRACT:     A class of recursive equations extending those of the form yn=(yn−2yn−1−1)/(yn−2+yn−1) is transformed into a special case of the nonlinear recursive equation xn=cxn−1h1(n)xn−2h2(n)...xnl+1hl−1(n)xnlhl(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