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On rational recursive sequences. (English) Zbl 0777.39002
The present study is related to the global asymptotic behavior, the oscillatory character and the periodic nature of all solutions of the rational recursive sequences;
\(x_{n+1}=[a+\sum^{k-1}_{i=0}b_ ix_{n-i}]/x_{n-k}\), and \(x_{n+1}=(a+bx_ n)/(A+x_{n-k})\), \(n=0,1,2,\dots\), which arises due to an open problem [problem # 1343, Math., Mag. 63, No. 2, 125 (1990)].

MSC:
39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
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