Infinite series for $\pi/3$ and other identities

TL;DR

This paper derives a novel infinite series formula for /3 using calculus and classical identities, and presents twenty-seven related identities involving  and other irrationals, celebrating Pi Day 2022.

Contribution

It introduces a new infinite series for /3 and provides twenty-seven related identities, expanding the set of known mathematical formulas involving  and irrationals.

Findings

New infinite series for /3 derived

Twenty-seven related identities involving  and irrationals presented

Series and identities are not well known and contribute to mathematical literature

Abstract

Using techniques from calculus, we combine classical identities for $\pi$, $\operatorname{ln}2$, and harmonic numbers, to arrive at a nice infinite series formula for $\pi/3$ that does not appear to be well known. In addition, we give twenty-seven related identities involving $\pi$ and other irrational numbers. Posted in celebration of Pi Day 2022.