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Explicit expressions for the related numbers of higher order Appell polynomials

2018/06/15 by Su Hu, Hu, Su, Takao Komatsu +1
Mathematics · #11B37 #11B68 #11C20 #15A15 #33C15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.06023

openalex publication_date 2018/06/15 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28

Abstract

In this note, by using the Hasse-Teichmüller derivatives, we obtain two explicit expressions for the related numbers of higher order Appell polynomials. One of them presents a determinant expression for the related numbers of higher order Appell polynomials, which involves several determinant expressions of special numbers, such as the higher order generalized hypergeometric Bernoulli and Cauchy numbers, thus recovers the classical determinant expressions of Bernoulli and Cauchy numbers stated in an article by Glaisher in 1875.

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