A natural companion to Catalan's constant

Abstract

. We consider here a trilogarithmic expression that plays a similar role to Catalan’s constant G in many ways: The main purpose of this article is to demonstrate how G is a naturally occurring and useful expression that deserves to be recognized as a mathematical constant and as a natural trilogarithmic “extension” of Catalan’s constant G . Having identi fi ed this constant, we evaluate many new and non-trivial integrals, Euler-type sums, p F q series, and binomial-harmonic series using G , extending known results on the classical version of Catalan’s constant.