Results 71 to 80 of about 207 (144)

A Study of the q-Truncated Exponential–Appell Polynomials

Mathematics
This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp.
Francesco Aldo Costabile, Subuhi Khan, Hassan Ali   +2 more
doaj   +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

On Appell-Laguerre polynomials

Journal of Computational and Applied Mathematics, 1993
The author considers so-called Appell-Laguerre polynomials, given explicitly by \[ Q_ n(x;k)=c_ n \sum_{j=0}^ n{(-n)_ j x^ j\over (\alpha+k+1-n)_ j j!} \quad (k,n \in {\mathcal N}). \] He gives a generating function and facts about the simplicity and location of the zeros; for the proofs the author refers to his paper Rodrigues' formula revisited ...
openaire   +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

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

On (self-) reciprocal Appell polynomials: Symmetry and Faulhaber-type polynomials

, 2021
17 pages, final revised ...
openaire   +4 more sources

Certain Properties and Characterizations of Generalized Gould–Hopper-Based Hybrid Polynomials

Mathematics
This study offers a comprehensive generalization of the Gould–Hopper polynomials and their Appell-type analogs. Employing the quasi-monomiality approach, we delineate fundamental analytical characteristics, including recurrence relations, associated ...
Waseem Ahmad Khan, Francesco Aldo Costabile, Can Kızılateş, Khidir Shaib Mohamed, Alawia Adam, Mona A. Mohamed   +5 more
doaj   +1 more source

Sheffer and Non-Sheffer Polynomial Families

International Journal of Mathematics and Mathematical Sciences, 2012
By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.
G. Dattoli, B. Germano, M. R. Martinelli, P. E. Ricci   +3 more
doaj   +1 more source

Generalizations of the Bernoulli and Appell polynomials

Abstract and Applied Analysis, 2004
We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions.
Gabriella Bretti, Pierpaolo Natalini, Paolo E. Ricci   +2 more
doaj   +1 more source