New results on p-Bernoulli numbers
Number Theory
2017-02-22 v1
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.
Cite
@article{arxiv.1702.06422,
title = {New results on p-Bernoulli numbers},
author = {Levent Kargın},
journal= {arXiv preprint arXiv:1702.06422},
year = {2017}
}