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

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.

23 pages

References in corpus (6)

• History of the formulas and algorithms for pi
• A formula for pi involving nested radicals
• An iteration procedure for a two-term Machin-like formula for pi with small Lehmer's measure
• The two-term Machin-like formula for pi with small arguments of the arctangent function
• Unconditional applicability of Lehmer's measure to the two-term Machin-like formula for $\pi$
• A new form of the Machin-like formula for pi by iteration with increasing integers