Bell polynomials and generalized Blissard problems

Bell polynomials and generalized Blissard problems

We introduce two possible generalizations of the classical Blissard problem and we show how to solve them by using the second order and multi-dimensional Bell polynomials, whose most important properties are recalled. © 2010 Elsevier Ltd. All rights reserved.

Generalized Bell Polynomials and the Combinatorics of Poisson Central Moments

We introduce a family of polynomials that generalizes the Bell polynomials, in connection with the combinatorics of the central moments of the Poisson distribution. We show that these polynomials are dual of the Charlier polynomials by the Stirling transform, and we study the resulting combinatorial identities for the number of partitions of a set into subsets of size at least 2.

Complete Bell polynomials and new generalized identities for polynomials of higher order

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of these identities is considered and generating function for polynomials satisfying this general identity is found.

Laguerre-type Bell polynomials

We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

Bell polynomials and Fibonacci numbers