HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS Zhong, Ting; Shen, Luming;
For generalized continued fraction (GCF) with parameter , we consider the size of the set whose partial quotients increase rapidly, namely the set , where > 1. We in  have obtained the Hausdorff dimension of when is constant or for any . As its supplement, now we show that: . So the bigger the parameter function is, the larger the size of becomes.
expansion;Engel series expansion;parameter function;growth rates;Hausdorff dimension;