The translated Dowling polynomials and numbers
type: Item
instance of: scholarly article
title: The translated Dowling polynomials and numbers
zbMATH Open document ID: 1460.05014
DOI: 10.1155/2014/678408
author: Mahid M. Mangontarum
author: Amila P. Macodi-Ringia
author: Normalah S. Abdulcarim
published in: International Scholarly Research Notices. Discrete Mathematics
publication date: 2019-02-21T00:00:00Z
review text: Summary: More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 7027205
Wikidata QID: Q42061818
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/678408
OpenAlex ID: W2065952498
cites work: On Whitney numbers of Dowling lattices
cites work: On some numbers related to Whitney numbers of Dowling lattices
cites work: Q5404347
cites work: Q4769056
cites work: A new formula for the Bernoulli polynomials
cites work: Q5310209
cites work: The \(r\)-Stirling numbers
cites work: \(r\)-Whitney numbers of Dowling lattices
cites work: Some results on Whitney numbers of Dowling lattices
cites work: On generalized Bell polynomials
cites work: The $r$-Bell numbers
cites work: Q4723747
cites work: Q3637645
cites work: Some aspects of Hankel matrices in coding theory and combinatorics
cites work: A characterization of the Bell numbers
cites work: Hankel determinant constructed on polynomials associated with the number of derangements
cites work: The Hankel Determinant of Exponential Polynomials
cites work: The Hankel transform and some of its properties
cites work: Asymptotic estimates for \(r\)-Whitney numbers of the second kind
description: scientific article; zbMATH DE number 7027205