Obtaining Concise Formulae on Bernoulli Polynomials-Numbers and Sums of Powers-Faulhaber Problems

Utilizing the rewording operator exp (aμz) to show Bernoulli polynomials Bm(z) and power sums Sm(z,n) as polynomials of Appell-type , we get concisely principal part their known properties as so as many new one, especially very plain symbolic formulae for

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Obtaining Easily Powers Sums on Arithmetic Progressions and Properties of Bernoulli Polynomials by Operator Calculus

We show that a sum of powers on an arithmetic progression is the transform of a monomial by a differential operator and that its generating function is simply related to that of the Bernoulli polynomials from which consequently it may

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