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18 February 2025
 
  » arxiv » 1508.0176

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The fastest possible continued fraction approximations of a class of functions
Xiaodong Cao ; Yoshio Tanigawa ; Wenguang Zhai ;
Date 2 Aug 2015
AbstractThe 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.
Source arXiv, 1508.0176
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