Exotic series with Bernoulli, harmonic, Catalan, and Stirling numbers

TL;DR

This paper introduces new closed-form series involving Bernoulli, harmonic, Catalan, Stirling numbers, and exponential polynomials, expanding the understanding of exotic series and their identities.

Contribution

It provides novel formulas for generating exotic series that incorporate multiple special number sequences and polynomials, evaluated in closed form.

Findings

Series identities with Laguerre and derangement polynomials

Closed-form evaluations of series involving special numbers

Extension of exotic series concepts in mathematical analysis

Abstract

In this paper, we present a formula for generating various exotic series in the spirit of Ovidiu Furdui and Alina Sintamarian. Our new series (evaluated in closed form) involve Bernoulli, harmonic, and Catalan numbers. Also Stirling numbers of the second kind, other special numbers, and exponential polynomials. The results include series identities with Laguerre polynomials and derangement polynomials.