A Series Representation for the Hurwitz–Lerch Zeta Function

Abstract

We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.

Keywords

• Hurwitz–Lerch zeta function
• incomplete gamma function
• Apéry’s constant
• Catalan’s constant
• exponential integral function
• Cauchy integral