New results on p-Bernoulli numbers

2017/02/20 by Levent Kargın, Kargın, Levent
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1702.06422

openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such as recurrence relations, telescopic formula and Raabe's formula to p-Bernoulli polynomials and numbers. In particular cases of these results, we establish some new results for Bernoulli polynomials and numbers. Moreover, we evaluate a Faulhaber-type summation in terms of p-Bernoulli polynomials.

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