Expression and dynamics of the solutions of some rational recursive sequences

Document Type: Regular Paper

Authors

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

In this paper we obtain the expression of the solutions of the following recursive sequences
􀝔
 
􀯡􀬾􀬵 􀵌
􀝔
 
􀯡􀬿􀬶􀝔􀯡􀬿􀬷􀝔􀯡􀬿􀬸
􀝔
 
􀯡􀝔􀯡􀬿􀬵􁈺􀵇1 􀵇 􀝔􀯡􀬿􀬶􀝔􀯡􀬿􀬷􀝔􀯡􀬿􀬸􁈻
, 􀝊 􀵌 0,1, . . .,
where the initial conditions are arbitrary real numbers. Also, we study the behavior of the solution of these
equations.

Keywords