A Survey on Orthogonal Polynomials from a Monomiality Principle Point of View [PDF]
EncyclopediaThis survey highlights the significant role of exponential operators and the monomiality principle in the theory of special polynomials. Using operational calculus formalism, we revisited classical and current results corresponding to a broad class of ...
Clemente Cesarano +2 more
doaj +6 more sources
Explicit relations on the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials and numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials by using monomiality principle and operational methods.
Burak Kurt
doaj +3 more sources
Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials [PDF]
Mathematics, 2023 A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions.
Mohra Zayed +2 more
doaj +2 more sources
Fractal and Fractional, 2023 The development of certain aspects of special polynomials in line with the monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research.
Rabab Alyusof, Shahid Ahmmad Wani
doaj +2 more sources
Differential Equations for Classical and Non-Classical Polynomial Sets: A Survey
Axioms, 2019 By using the monomiality principle and general results on Sheffer polynomial sets, the differential equation satisfied by several old and new polynomial sets is shown.
Paolo Emilio Ricci
doaj +2 more sources
On monomiality property of q-Gould-Hopper-Appell polynomials
Arab Journal of Basic and Applied SciencesRecently, in the theory of q-special functions, the extension of the monomiality concept to q-special polynomials is introduced. This extension can be a beneficial tool for considering the quasi-monomiality of certain q-special polynomials.
Nusrat Raza, Mohammed Fadel, Subuhi Khan
doaj +3 more sources
Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials
Mathematics, 2023 The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials.
Shahid Ahmad Wani +3 more
doaj +1 more source
Degenerate 2D bivariate Appell polynomials: properties and applications
Applied Mathematics in Science and Engineering, 2023 The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable.
Shahid Ahmad Wani +2 more
doaj +1 more source
Construction of a new family of Fubini-type polynomials and its applications
Advances in Difference Equations, 2021 This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials ...
H. M. Srivastava +5 more
doaj +1 more source
Certain results on a hybrid class of the Boas–Buck polynomials
Advances in Difference Equations, 2020 This article aims to introduce a hybrid family of 2-variable Boas–Buck-general polynomials by taking Boas–Buck polynomials as a base with the 2-variable general polynomials.
Ghazala Yasmin +2 more
doaj +1 more source