2 research outputs found
Continued fraction expression of the Mathieu series
In this paper, we represent a continued fraction expression of Mathieu series
by a continued fraction formula of Ramanujan. As application, we obtain some
new bounds for Mathieu series
Multiple-correction and summation of the rational series
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