Irrational Acceleration of a Continued Fraction of $\pi$

TL;DR

The paper introduces a novel application of Bauer-Muir acceleration to derive an irrational continued fraction for pi, achieving faster convergence and extending the method to other constants like ln(2) and cube root of 2.

Contribution

It presents a new accelerated continued fraction for pi with irrational coefficients, expanding the Bauer-Muir method to more constants and higher-dimensional matrix representations.

Findings

Faster convergence of the continued fraction for pi.

Extension of the method to ln(2) and ³√2.

Representation as a generalized continued fraction with increased dimension.

Abstract

An application of (iterated) Bauer-Muir acceleration can give an Ap\'ery-like continued fraction for $\pi$ with irrational coefficients, and much faster convergence. It can be considered a generalized continued fraction with the same matrix representation as the standard case, but the dimension increased due to irrationality. The construction is also given for $\ln(2)$ and $\sqrt[3]{2}$.