Results 31 to 40 of about 105 (94)

Linear Algebraic Approach to Formulate A New Recurrence Relation for Bernoulli Numbers from the Power-Sum of Natural Numbers with Experiments on Pedagogy

, 2021
In this article, a new recurrence relation formula for Bernoullinumbers have been derived, and sum of integer exponents of natural numbershas been revisited from this novel perspective.
Sumit Bhowmick; Department of Materials and Metallurgical Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000,, Md. Shafiqul Islam; Department of Materials and Metallurgical Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000,   +1 more
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Probabilistic degenerate Bernstein polynomials

Applied Mathematics in Science and Engineering
In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier.
Jinyu Wang, Yuankui Ma, Taekyun Kim, Dae San Kim   +3 more
doaj   +1 more source

On a family of q-modified-Laguerre-Appell polynomials

Arab Journal of Basic and Applied Sciences
This paper aims to introduce a new class of special polynomials called q-modified Laguerre-Appell polynomials. Some definitions and concepts related to this class of polynomials, including generating function and series definition are explored.
Mohammed Fadel, Abdulghani Muhyi
doaj   +1 more source

Probabilistic identities involving fully degenerate Bernoulli polynomials and degenerate Euler polynomials

Applied Mathematics in Science and Engineering
Assume that X is the Bernoulli random variable with parameter [Formula: see text], and that random variables [Formula: see text] are a sequence of mutually independent copies of X.
Taekyun Kim, Dae San Kim, Jongkyum Kwon
doaj   +1 more source

Identities involving degenerate stirling numbers of the second kind

Mathematical and Computer Modelling of Dynamical Systems
Building on Carlitz’s foundational work with degenerate Euler and Bernoulli polynomials, recent research has introduced and studied various degenerate special numbers and polynomials.
Taekyun Kim, Dae San Kim, Murad Khalil, Kyo-Shin Hwang   +3 more
doaj   +1 more source

Generalized apostol-type polynomial matrix and its algebraic properties [PDF]

, 2019
The aim of this paper is to introduce the generalized Apostol-type polynomial matrix W [m−1,α](x;c,a;λ;µ;ν) and the generalized Apos-tol-type matrix W [m−1,α](c,a;λ;µ;ν).
Ramírez, William, Quintana, Yamilet, Urieles Guerrero, Alejandro   +2 more
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Probabilistic degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
Recently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo, Taekyun Kim, Dae San Kim, Yuankui Ma   +3 more
doaj   +1 more source

Computing a family of probabilistic numbers in terms of probabilistic Stirling numbers of the second kind

Applied Mathematics in Science and Engineering
In this paper, we introduce the probabilistic Bernoulli numbers, Cauchy numbers, and Euler numbers of order α associated with the random variable Y, utilizing the generating function approach.
Aimin Xu
doaj   +1 more source

Bivariate q-Laguerre–Appell polynomials and their applications

Applied Mathematics in Science and Engineering
Recently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered.
Mohammed Fadel, Nusrat Raza, Ahmed Al-Gonah, Ugur Duran   +3 more
doaj   +1 more source

A closed formula for the generating function of p-Bernoulli numbers

, 2018
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the nite summation of Bernoulli and harmonic ...
Rahmani, Mourad, Kargin, Levent, Levent Kargin, Mourad Rahmani   +3 more
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