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Corpus ID: 119321782

Multiple-correction and summation of the rational series

@article{Cao2015MultiplecorrectionAS,
title={Multiple-correction and summation of the rational series},
author={Xiaodong Cao and C. Mortici},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}

The goal of this work is to formulate a systematical method for looking for the simple closed form or continued fraction representation of a class of rational series. As applications, we obtain the continued fraction representations for the alternating Mathieu series and some rational series. The main tools are multiple-correction and two of Ramanujan's continued fraction formulae involving the quotient of the gamma functions.