Dirichlet series and series with Stirling numbers

TL;DR

This paper derives new identities involving Dirichlet series and series with Stirling numbers, utilizing various special number sequences as coefficients to expand the mathematical understanding of these series.

Contribution

It introduces novel identities connecting Dirichlet series with Stirling numbers and special number sequences, expanding theoretical knowledge in this area.

Findings

Derived identities for Dirichlet series with Stirling numbers

Connected special number sequences as coefficients in these series

Enhanced understanding of series involving Stirling and related 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.