Some metric properties on the GCF fraction expansion

In Schweiger (2003) [1], , Fritz Schweiger introduced the algorithm of the generalized continued fraction (GCF), and in Zhong (2008) [2], T. Zhong studied some basic metric properties of the GCF. In this paper, under the restriction of −1<ε(k)⩽1, the “0–1” law and the central limit theorem of quotients in the GCF expansions are studied.