Dirichlet series and series with Stirling numbers

Abstract

This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers, binomial coefficients, central binomial coefficients, and Catalan numbers.

Keywords

• series identities
• stirling numbers of the first kind
• harmonic numbers
• hyperharmonic numbers
• cauchy numbers
• derangement numbers
• catalan numbers
• central binomial coefficients