Some carlitz type identities for the Bernoulli number of the second kind

Jamel Chikhi (1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

In this short note, we obtain some identities for the Bernoulli numbers of the second kind. They are similar to the Carlitz's type recurrence relations for the (ordinary) Bernoulli numbers, in convolution symbolic notation, (−1)^m (B n + 1)^m = (−1)^n (B m + 1)^n. The proof is quite simple and uses the method of generating functions.

Mots clés: falling factorials; Carlitz identities

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Jamel Chikhi. Some carlitz type identities for the Bernoulli number of the second kind. 2020. ⟨hal-02536464⟩