A method to reduce the Lehmer measure in a multi-term Machin-like formula for $\pi$

TL;DR

This paper introduces a new method to generate multi-term Machin-like formulas for pi with lower Lehmer measures, improving the efficiency of such formulas.

Contribution

It presents a novel approach to reduce the Lehmer measure in multi-term Machin-like formulas for pi, enhancing computational efficiency.

Findings

Successfully generated formulas with lower Lehmer measures

Validated results using Mathematica code

Improved efficiency of pi computation formulas

Abstract

Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for $\pi$. As a further development, here we show how to generate a multi-term Machin-like formula for $\pi$ with a reduced Lehmer measure. The Mathematica codes validating these results are presented.