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Related papers: Probabilistic bivariate Bell polynomials

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The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral…

Number Theory · Mathematics 2020-12-10 Taekyun Kim , Dae san Kim

In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…

Number Theory · Mathematics 2018-09-27 Tuba Çakmak , Erdal Karaduman

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…

Classical Analysis and ODEs · Mathematics 2008-12-22 Michael R. Hoare , Mizan Rahman

The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other…

Number Theory · Mathematics 2020-08-11 Dae San Kim , Taekyun Kim

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…

Number Theory · Mathematics 2021-08-16 Taekyun Kim , Dae San Kim , Hyunseok Lee , Seongho Park

The notion of generalized Bell numbers has appeared in several works but there is no systematic treatise on this topic. In this paper we fill this gap. We discuss the most important combinatorial, algebraic and analytic properties of these…

Combinatorics · Mathematics 2010-01-09 Istvan Mezo

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…

Number Theory · Mathematics 2015-07-09 Taekyun Kim , Dae san Kim

We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…

Combinatorics · Mathematics 2017-10-10 Tanay Wakhare

Recently, several types of degenerate Bell polynomials have been introduced as degenerate versions of the ordinary Bell polynomials. The aim of this paper is to study some identities for the degenerate Bell polynomials and their related…

Number Theory · Mathematics 2021-12-17 Taekyun Kim , Dae san kim

Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via…

Number Theory · Mathematics 2022-08-11 Taekyun Kim , Dae san Kim , Hye Kyung Kim

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…

Data Analysis, Statistics and Probability · Physics 2007-05-23 M. Hisakado , K. Kitsukawa , S. Mori

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…

Number Theory · Mathematics 2009-11-17 Boris Y. Rubinstein

Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey's type recurrence relations for the degenerate Bell polynomials and the degenerate Dowling polynomials by using…

Number Theory · Mathematics 2025-03-05 Taekyun Kim , Dae San Kim

Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…

Number Theory · Mathematics 2017-05-24 Taekyun Kim , Dae san Kim

A new explicit closed-form formula for the multivariate $(n, k)$th partial Bell polynomial $B_{n,k} (x_1, x_2, ..., x_{n - k + 1})$ is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily…

Classical Analysis and ODEs · Mathematics 2013-01-17 Djurdje Cvijovic

Partial multivariate Bell polynomials have been defined by E.T. Bell in 1934. These polynomials have numerous applications in Combinatorics, Analysis, Algebra, Probabilities, etc. Many of the formulae on Bell polynomials involve…

Combinatorics · Mathematics 2016-01-25 Ammar Aboud , Jean-Paul Bultel , Ali Chouria , Jean-Gabriel Luque , Olivier Mallet

We show that Bell correlations may arise as a special sort of selection artefact, produced by ordinary control of the initial state of the experiments concerned. This accounts for nonlocality, without recourse to any direct spacelike…

Quantum Physics · Physics 2024-03-14 Huw Price , Ken Wharton

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

Probability · Mathematics 2026-05-15 Palaniappan Vellaisamy , Puja Pandey

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

Classical Analysis and ODEs · Mathematics 2011-05-03 Roland Groux

A sequence of coefficients appearing in a recurrence for the Narayana polynomials is generalized. The coefficients are given a probabilistic interpretation in terms of beta distributed random variables. The recurrence established by M.…

Number Theory · Mathematics 2012-03-21 T. Amdeberhan , V. H. Moll , C. Vignat