The fastest possible continued fraction approximations of a class of functions
Classical Analysis and ODEs
2015-08-04 v1
Abstract
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 the gamma functions, which is showed to be the fastest possible. Finally, three conjectures are proposed.
Keywords
Cite
@article{arxiv.1508.00176,
title = {The fastest possible continued fraction approximations of a class of functions},
author = {Xiaodong Cao and Yoshio Tanigawa and Wenguang Zhai},
journal= {arXiv preprint arXiv:1508.00176},
year = {2015}
}