Geodesic
Carlitz-type and other Bernoulli identities
Journal of integer sequences, Tome 19 (2016) no. 1
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)$^{n}, r = 1, \dots , K + 1$, 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.
Classification : 11B68, 05A10
Keywords: Bernoulli number, Bernoulli polynomial, Bernoulli identity 
@article{JIS_2016__19_1_a5,
     author = {de J.Pita Ruiz V.,  Claudio},
     title = {Carlitz-type and other {Bernoulli} identities},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {1},
     zbl = {1364.11058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a5/}
}
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de J.Pita Ruiz V.,  Claudio. Carlitz-type and other Bernoulli identities. Journal of integer sequences, Tome 19 (2016) no. 1. http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a5/