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}
}

• Xiaodong Cao, Y. Tanigawa, W. Zhai
• Published 2015
• Mathematics
• arXiv: Classical Analysis and ODEs

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

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