Results 221 to 230 of about 34,757 (249)

Multivariate Bell polynomials

International Journal of Computer Mathematics, 2010
The multivariate Bell polynomials are defined as the coefficients of a power of a multivariate series. We give recurrence relations for them and examples for dimensions 2 and 3.
Christopher S. Withers, Saralees Nadarajah   +1 more
openaire   +2 more sources

Bell polynomials

ACM SIGSAM Bulletin, 1987
An introduction to Bell polynomials is given in order to see how they can be used to compute some of the classical counting functions of Combinatorics. They are also used to compute the Taylor coefficients of formal power series given as a composition of two power series along with computing the composition inverse of a power series.
openaire   +2 more sources

A probabilistic interpretation of the Bell polynomials

Stochastic Analysis and Applications, 2021
In this paper, we obtain a probabilistic relationship between the exponential Bell polynomials and the weighted sums of independent Poisson random variables.
Palaniappan Vellaisamy, K. K. Kataria, Vijay Kumar   +2 more
openaire   +2 more sources

A generalized ordered Bell polynomial

Linear Algebra and its Applications, 2020
Abstract In this paper, we consider a generalized ordered Bell polynomial P n ( q ) defined by the following exponential generating function ∑ n ≥ 0 P n ( q ) n ! t n = e γ t ( β β + β ′ q − β ′ q e t β ) 1 + γ ′ β ′ .
Wan-Ming Guo, Bao-Xuan Zhu
openaire   +2 more sources

The estimation of the zeros of the Bell and r-Bell polynomials

Applied Mathematics and Computation, 2015
Abstract It is a classical result that the zeros of the Bell polynomials are real and negative. In this study we deal with the asymptotic growth of the leftmost zeros of the Bell polynomials and generalize the results for the r-Bell polynomials, too.
István Mező, Roberto B. Corcino
openaire   +2 more sources

The Bell Differential Polynomials

1998
Let A be an associative algebra with a unit element 1. If A is commutative then there holds the well-known binomial law $$ (x + y)n = \sum\limits_{k = 0}^n {(_k^n} {)_x}n - {k_y}k $$ (1) where formally x 0 = 1, y 0 = 1. Our aim is to generalize the binomial law to the case where A is not necessarily commutative.
R. Schimming, Saad Zagloul Rida
openaire   +2 more sources

On degenerate Bell numbers and polynomials

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016
Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new identities of those numbers and polynomials associated with special numbers and polynomials.
Dae San Kim, Taekyun Kim
openaire   +2 more sources

Combinants, Bell polynomials and applications

Journal of Physics A: Mathematical and General, 1984
The concept of combinants introduced in the formulation of the generating function for probabilities is analysed, demonstrating the fact that they play the same role in computing cumulants as probabilities do in computing moments. The mathematical framework of Bell polynomials is used to relate combinants and probabilities.
K V Parthasarathy, R Vasudevan, P R Vittal   +2 more
openaire   +2 more sources

On hermite-bell inverse polynomials

Rendiconti del Circolo Matematico di Palermo, 1984
Hermite-Bell inverse polynomials are introduced and an ordinary differential equation which they obey is derived.
openaire   +2 more sources

A convolution involving Bell polynomials

Mathematical Proceedings of the Cambridge Philosophical Society, 1973
AbstractA convolution formula is established for Bell polynomials. This is expressed in seven equivalent ways and used to derive further properties of these polynomials. The application of these results to some twenty-seven special polynomial sets is shown and illustrated in the case of binomial, Hermite, Gegenbauer and generalized Bernoulli sets.
openaire   +2 more sources