A closed formula for the generating function of p-Bernoulli numbers. Issue 7 (3rd October 2018)

• Record Type: Journal Article
• Authors: Kargin, Levent; Rahmani, Mourad
• Is Part Of: Quaestiones mathematicae. Volume 41:Issue 7(2018)
• Page Start: 975
• Page End: 983
• Publication Date: 2018-10-03
• Subjects: 11B68 -- 11B83; Bernoulli polynomials and Bernoulli numbers -- generating functions -- geometric polynomials -- harmonic numbers -- Stirling numbers of the first and second kind; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2017.1418762
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: In this paper, using geometric polynomials, we obtain a generating function of p -Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving Stirling numbers of the second kind. We also give a relationship between the p -Bernoulli numbers and the generalized Bernoulli polynomials.