Some metric properties on the GCF fraction expansion (Q1038477)

This paper studies a generalization of continued fractions. \textit{F. Schweiger} [Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 212, 69--77 (2003; Zbl 1113.11045)] introduced the algorithm of the generalized continued fraction (GCF), and \textit{T. Zhong} [J. Number Theory 128, No. 6, 1506--1515 (2008; Zbl 1142.11061)] studied some basic metric properties of the GCF. In this paper, under the restriction of \(- 1<\varepsilon (k)\leq 1\), the ``0-1'' law and the central limit theorem of quotients in the GCF expansions is given and certain other asymptotic properties are established.