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

2021/10/02 by Khristo N. Boyadzhiev, Boyadzhiev, Khristo N.
Mathematics · Physics and Astronomy · #11B68 #11B73 #11C08 #40D05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.CO #math.NT #msc:11B68 #msc:11B73 #msc:11C08 #msc:40D05

paper · pdf · doi:10.48550/arxiv.2110.00689

16 pages

arxiv created 2021/10/02 · openalex publication_date 2021/10/02 · arxiv updated 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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