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Article overview
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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 | 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. | Source: | arXiv, 1508.0176 | Services: | Forum | Review | PDF | Favorites |
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