The Translated Dowling Polynomials and Numbers. (22nd December 2014)

• Record Type: Journal Article
• Authors: Mangontarum, Mahid M.; Macodi-Ringia, Amila P.; Abdulcarim, Normalah S.
• Other Names: Dondi Riccardo Academic Editor.
• Is Part Of: ISRN obstetrics and gynecology. Volume 2014(2014)
• Publication Date: 2014-12-22
• Subjects: Obstetrics -- Periodicals; Gynecology -- Periodicals; Pregnancy Complications; Genital Diseases, Female; Gynecology; Obstetrics; Electronic journals; Periodical; Periodicals; Fulltext; Internet Resources; Periodicals; 618.2
• DOI: 10.1155/2014/678408
• Languages: English
• ISSNs: 2090-4436

Abstract

Abstract : 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.