On a generalization of Euler's constant

Abstract

A one parameter generalization of Euler's constant γ from [Numer. Algorithms 46(2) (2007) 141--151] is investigated, and additional expressions for γ are derived. Included are forms involving the Gregory coefficients and the Hurwitz Zeta function, and expressions of the later are shown to lead to an alternative proof of Lerch's limit formula for the gamma function.

Keywords

• euler's constant
• gamma function
• hurwitz zeta function