Multiple-Correction and Continued Fraction Approximation

TL;DR

This paper advances a multiple-correction method to improve continued fraction approximations and refines existing results for constants like Landau, Lebesgue, and Euler-Mascheroni, demonstrating enhanced accuracy.

Contribution

It develops a new multiple-correction approach and applies it to improve continued fraction approximations for several mathematical constants.

Findings

Hybrid-type continued fraction approximations for Landau and Lebesgue constants

Refined bounds for the Euler-Mascheroni constant

Enhanced accuracy of constant approximations

Abstract

The main aim of this paper is to further develop a multiple-correction method formulated in a previous work~\cite{CXY}. As its applications, we find a kind of hybrid-type finite continued fraction approximations in two cases of Landau constants and Lebesgue constants. In addition, we refine the previous results of Lu~\cite{Lu} and Xu and You~\cite{XY} for the Euler-Mascheroni constant.