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Corpus ID: 119331787

The fastest possible continued fraction approximations of a class of functions

@article{Cao2015TheFP,
title={The fastest possible continued fraction approximations of a class of functions},
author={Xiaodong Cao and Y. Tanigawa and W. Zhai},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}

The goal of this paper is to formulate a systematical method for constructing the fastest possible continued fraction approximations of a class of functions. The main tools are the multiple-correction method, the generalized Mortici's lemma and the Mortici-transformation. As applications, we will present some sharp inequalities, and the continued fraction expansions associated to the volume of the unit ball. In addition, we obtain a new continued fraction expansion of Ramanujan for a ratio of… Expand