Obtaining Concise Formulae on Bernoulli Polynomials-Numbers and Sums of Powers-Faulhaber Problems | Chapter 2 | Research Highlights in Mathematics and Computer Science Vol. 6

 Utilizing the interpretation operator exp (aμz)  to show Bernoulli polynomials Bm(z) and power sums  Sm(z,n) as polynomials of Appell-type , we acquire concisely principal part their known properties as so as many new one, especially very natural symbolic formulae for wily Bernoulli numbers and polynomials, power sums of whole and complex numbers. Then by the change of debates from z into  Z = z(z-1) and n into λ that is the 1st order power total we obtain the Faulhaber recipe for powers sums  in term of polynomials in λ having coefficients contingent upon Z. Practically we give tables for wily in easiest attainable manners Tables of Bernoulli numbers, Bernoulli polynomials, sums of capacities of complex numbers are given.

Author(s) Details:

Do Tan Si,
The HoChiMinh-City Physical Association, Vietnam and ULB and UEM, Belgium.

Please see the link here: https://stm.bookpi.org/RHMCS-V6/article/view/9677