Tag: Bernoulli numbers

Utilizing the translation operator exp (aμz)  to represent Bernoulli polynomials Bm(z) and power sums  Sm(z,n) as polynomials of Appell-type , we obtain concisely almost all their known properties as so as many new ones, especially very simple symbolic formulae for calculating Bernoulli numbers and polynomials, power sums of entire...

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 be calculated. Besides, we show that it is obtainable...

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