Recurrence formulas with gaps for Bernoulli and Euler polynomials

2014/03/03 by Zhi-Hong Sun, Sun, Zhi-Hong
Mathematics · #11B39 #11B68 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1403.0435

openalex publication_date 2014/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \B_n\, \B_n(x)\ and \E_n(x)\ be the Bernoulli numbers, Bernoulli polynomials and Euler polynomials, respectively. In this paper we mainly establish formulas for ∑_{6| k-3}\binom nkB_n-k(x), ∑_{6| k}\binom nkE_n-k(x) and ∑_{6| k-3}\binom nkm^kB_n-k in the cases m=2,3,4.

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