Monomiality Principle and Eigenfunctions of Differential Operators [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We apply the so-called monomiality principle in order to construct eigenfunctions for a wide set of ordinary differential operators, relevant to special functions and polynomials, including Bessel functions and generalized Gould-Hopper polynomials.
Isabel Cação, Paolo E. Ricci
doaj +7 more sources
Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle [PDF]
Applied Mathematics and Computation, 2014 With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework with Lie-algebraic symmetries.
Faustino, Nelson
core +5 more sources
A Survey on Orthogonal Polynomials from a Monomiality Principle Point of View
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 +5 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
Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering [PDF]
Physics Letters A, 2005 We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus.
Blasiak, P +3 more
core +4 more sources
Construction of a new family of Fubini-type polynomials and its applications [PDF]
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 +2 more sources
Truncated-exponential-based Frobenius–Euler polynomials [PDF]
Advances in Difference Equations, 2019 In this paper, we first introduce a new family of polynomials, which are called the truncated-exponential based Frobenius–Euler polynomials, based upon an exponential generating function.
Wiyada Kumam +4 more
doaj +2 more sources
Two-Variable q-General-Appell Polynomials Within the Context of the Monomiality Principle
MathematicsIn this study, we consider the two-variable q-general polynomials and derive some properties. By using these polynomials, we introduce and study the theory of two-variable q-general Appell polynomials (2VqgAP) using q-operators.
Noor Alam +3 more
doaj +3 more sources
Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials
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 +1 more source
On an Umbral Point of View of the Gaussian and Gaussian-like Functions [PDF]
, 2023 The theory of Gaussian functions is reformulated using an umbral point of view. The symbolic method we adopt here allows an interpretation of the Gaussian in terms of a Lorentzian image function.
Dattoli G., Di Palma E., Licciardi S.
core +4 more sources