Multiple-correction and continued fraction approximation(II)

Abstract: 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.