Abstract:
By using an explicit formula for Bernoulli polynomials we obtained in a recent work (in which B n (x) is written as a linear combination of the polynomials (x − r) n , r = 1,. .. , K + 1, where K ≥ n), it is possible to obtain Bernoulli polynomial identities from polynomial-combinatorial identities. Using this approach, we obtain some generalizations and new demonstrations of the 1971 Carlitz identity involving Bernoulli numbers, and we also obtain some new identities involving Bernoulli polynomials.
Description:
By using an explicit formula for Bernoulli polynomials we obtained in a recent work (in which B n (x) is written as a linear combination of the polynomials (x − r) n , r = 1,. .. , K + 1, where K ≥ n), it is possible to obtain Bernoulli polynomial identities from polynomial-combinatorial identities. Using this approach, we obtain some generalizations and new demonstrations of the 1971 Carlitz identity involving Bernoulli numbers, and we also obtain some new identities involving Bernoulli polynomials.