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The fastest possible continued fraction approximations of a class of functions

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.

preprint2015arXivOpen access
Xiaodong CaoYoshio TanigawaWenguang Zhai
math.CA
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Open access3 authors1 topic
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Xiaodong CaoYoshio TanigawaWenguang Zhai

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