New series identities with Cauchy, Stirling, and harmonic numbers, and Laguerre polynomials

2019/10/31 by Khristo N. Boyadzhiev, Boyadzhiev, Khristo N. · 1 citation
Mathematics · #11B65 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11B65

paper · pdf · doi:10.48550/arxiv.1911.00186

17 pages

openalex publication_date 2019/10/31 · arxiv created 2022/01/08 · arxiv updated 2022/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we use an interplay between Newton series and binomial formulas in order to generate a number of series identities involving Cauchy numbers, harmonic numbers, Laguerre polynomials, and Stirling numbers of the first kind.

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• Convolutions for Stirling numbers, Lah numbers, and binomial coefficients

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