New BBP-Type Formulae for π Derived from New Forms of Taylor Expansions of Inverse Tangent Function

Abstract

In this work, we give two new Taylor expansions of arctan(x + ω), where ω represents a finite increment of x. We discover several remarkable infinite series from these expansions by special substitutions. Some of these infinite series give BBP-type formulae.

Keywords

• BBP-type formula
• Taylor expansion
• infinite series