Results 71 to 80 of about 528 (133)

Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials

Applied Mathematics in Science and Engineering
This article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
doaj   +1 more source

Fractional Operator Approach and Hybrid Special Polynomials: The Generalized Gould–Hopper–Bell-Based Appell Polynomials and Their Characteristics

Fractal and Fractional
This study introduces a novel generalized class of special polynomials using a fractional operator approach. These polynomials are referred to as the generalized Gould–Hopper–Bell-based Appell polynomials.
Rabeb Sidaoui, E. I. Hassan, Abdulghani Muhyi, Khaled Aldwoah, A. H. A. Alfedeel, Khidir Shaib Mohamed, Alawia Adam   +6 more
doaj   +1 more source

Adjoint Appell-Euler and First Kind Appell-Bernoulli Polynomials

, 2019
The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials.
P. Natalini, P. E. Ricci, Ricci, Paolo E., Natalini, Pierpaolo   +3 more
core  

Approximation by Operators Including Generalized Appell Polynomials

, 2016
In this work, the problem of the approximation by certain polynomials is addressed. A new type operators sequence including generalized Appell polynomials are defined, qualitative and quantitative approximation theorems are proved. Some explicit examples
Icoz, Gurhan and Varma, Serhan and Sucu, Sezgin
core   +1 more source

Exploring Extended Degenerate Bell-Based Appell Polynomials via Fractional Operators: Properties, Determinant Representations, and Numerical Illustrations

Mathematics
This paper introduces a new family of extended degenerate Bell-based Appell polynomials by applying Euler’s integral as a fractional operator to the Appell-type degenerate Bell polynomials.
Mohra Zayed, Ines Ben Omrane, Francesco Aldo Costabile, Mdi Begum Jeelani, Shahid Ahmad Wani   +4 more
doaj   +1 more source

Investigating the Properties and Dynamic Applications of Δ_h Legendre–Appell Polynomials

Mathematics
This research aims to introduce and examine a new type of polynomial called the Δh Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δh Legendre–Appell polynomials and explore their properties.
Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Hasan Nihal Zaidi   +3 more
doaj   +1 more source

A unified matrix approach to the representation of Appell polynomials

, 2014
In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix which has only the natural numbers as entries and is closely related to the ...
Tomaz, Graça, Malonek, Helmuth R., Aceto, L., Tomaz, G., Aceto, Lidia, Malonek, H. R.   +5 more
core   +1 more source

Umbral Calculus and the Frobenius-Euler Polynomials

Abstract and Applied Analysis, 2013
We study some properties of umbral calculus related to the Appell sequence. From those properties, we derive new and interesting identities of the Frobenius-Euler polynomials.
Dae San Kim, Taekyun Kim, Sang-Hun Lee
doaj   +1 more source

Two-Parameter Identities for q-Appell Polynomials

, 2023
In this paper, by using the techniques of the q-exponential generating series, we extend a well-known two-parameter identity for the Appell polynomials to the q-Appell polynomials of type I and II.
Munarini E.
core  

Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers

Mathematics
In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s-Appell polynomials related to Stirling numbers and binomial coefficients.
Tian-Xiao He, Emanuele Munarini
doaj   +1 more source