Documentación técnica
Carlitz-Type and Other Bernoulli Identities
Autor
Madsen, Søren Møller
Institución
Resumen
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. 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.