Asymptotic behaviour of a sequence defined by iteration. (English) Zbl 1032.40002

Stević, Stevo

Mat. Vesn. 48, No. 3-4, 99-105 (1996).

Asymptotic behaviour of a sequence \(x_n=f(x_{n-1})\), \(n\in\mathbb{N}\), where \(f(x)=x-ax^k+bx^{k+p}+o(x^{k+p})\) around \(0+\), is given for various \(p\) and \(k\). The results generalize old (solved) problems of Pólya and Szegö, and Cox. Interesting examples are given.

Reviewer: Stevan Pilipović (Novi Sad)

MSC:

40A05

Convergence and divergence of series and sequences