Si, D.T. (2019) The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked. Applied Mathematics, 10, 100-112.
https://doi.org/10.4236/am.2019.103009

has been cited by the following article:

• TITLE: Selection of Coherent and Concise Formulae on Bernoulli Polynomials-Numbers-Series and Power Sums-Faulhaber Problems

  AUTHORS: Do Tan Si

  KEYWORDS: Bernoulli Numbers, Bernoulli Polynomials, Powers Sums, Zeta Function, Faulhaber Conjecture

  JOURNAL NAME: Applied Mathematics, Vol.13 No.10, October 28, 2022

  ABSTRACT: Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursion relations for calculating Bernoulli polynomials and numbers, new formulae for obtaining power sums of entire and complex numbers. Then by the change of arguments from z into Z = z(z-1) and n into λ which is the 1st order power sum we obtain the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. Practically we give tables for calculating in easiest possible manners, the Bernoulli numbers, polynomials, the general powers sums.