Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables
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DOI: 10.1155/2020/6624006
Abstract: The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708. A derangement is a permutation that has no fixed points, and the derangement number D n is the number of fixed… read more here.
Keywords: identities involving; random variables; polynomials numbers; gamma random ... See more keywords
Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol-Bernoulli Polynomials and Numbers, and Degenerate Apostol-Euler Polynomials and Numbers
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DOI: 10.3390/axioms11090477
Abstract: In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for… read more here.
Keywords: type polynomials; degenerate apostol; polynomials numbers; fubini type ... See more keywords
New Families of Three-Variable Polynomials Coupled with Well-Known Polynomials and Numbers
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DOI: 10.3390/sym11020264
Abstract: In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit… read more here.
Keywords: new families; polynomials numbers; three variable; families three ... See more keywords
On Generating Functions for Boole Type Polynomials and Numbers of Higher Order and Their Applications
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DOI: 10.3390/sym11030352
Abstract: The purpose of this manuscript is to study and investigate generating functions for Boole type polynomials and numbers of higher order. With the help of these generating functions, many properties of Boole type polynomials and… read more here.
Keywords: type polynomials; boole type; generating functions; polynomials numbers ... See more keywords
On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers
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DOI: 10.3390/sym14040654
Abstract: The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials, the… read more here.
Keywords: parametrically generalized; euler polynomials; functions parametrically; polynomials numbers ... See more keywords