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The main aim of this paper is to further develop the multiple-correction method that formulated in our previous works~cite{CXY, Cao}. As its applications, we establish a kind of hybrid-type finite continued fraction approximations related to BBP-type series of the constant $pi$ and other classical constants, such as Catalan constant, $pi^2$, etc.
We show that the growth rate of denominator $Q_n$ of the $n$-th convergent of negative expansion of $x$ and the rate of approximation: $$ frac{log{n}}{n}log{left|x-frac{P_n}{Q_n}right|}rightarrow -frac{pi^2}{3} quad text{in measure.} $$ for a.e. $x$.
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.
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 Morticis lemma and the Mo
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 alternati
We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arnoux and Nogueira. We also apply the same method on the unsorted versio