Notes on two kinds of special values for the Bell polynomials of the second kind

Feng Qi (1, 2, 3) , Dongkyu Lim (4) , Yong-Hong Yao (1)

1 Tianjin Polytechnic University
2 Inner Mongolia University for Nationalities
3 Henan Polytechnic University
4 Andong National University

In the paper, by methods and techniques in combinatorial analysis and the theory of special functions, the authors discuss two kinds of special values for the Bell polynomials of the second kind for two special sequences, find a relation between these two kinds of special values for the Bell polynomials of the second kind, and derive an identity involving the combinatorial numbers.

Mots clés: special value; Vandermonde convolution formula; combinatorial analysis; beta function; identity; Faa di Bruno formula; relation; factorial; Bell polynomial of the second kind

Domaines: Combinatoire [math.CO]; Analyse classique [math.CA]

Feng Qi, Dongkyu Lim, Yong-Hong Yao. Notes on two kinds of special values for the Bell polynomials of the second kind: Notes on special values of the Bell polynomials. Miskolc Mathematical Notes, 2019, 20 (1), pp.465--474. ⟨10.18514/MMN.2019.2635⟩. ⟨hal-01757740v2⟩