Abstract
On analogy of the regular continued fractions, for any fixed positive integer [Formula: see text], every [Formula: see text] can be expanded into an [Formula: see text]-continued fraction, denoted by [Formula: see text], where [Formula: see text] are called the partial quotients. In this paper, we concern the metric theory of the partial quotients. More precisely, let [Formula: see text], the Borel–Bernstein theorem and Hausdorff dimension of the set [Formula: see text] for infinitely many [Formula: see text] are determined. This generalizes the results of regular continued fractions.
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