Results 1 to 10 of about 1,365,933 (128)

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   +10 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   +7 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, Dattoli, G, Horzela, A, Penson, K A   +3 more
core   +8 more sources

Two-Variable q-General-Appell Polynomials Within the Context of the Monomiality Principle [PDF]

Mathematics
In 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, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +5 more sources

A Survey on Orthogonal Polynomials from a Monomiality Principle Point of View

Encyclopedia
This 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, Yamilet Quintana, William Ramírez   +2 more
doaj   +5 more sources

Quasi-Monomiality Principle and Certain Properties of Degenerate Hybrid Special Polynomials [PDF]

Symmetry, 2023
This article aims to introduce degenerate hybrid type Appell polynomials HQm(u,v,w;η) and establishes their quasi-monomial characteristics. Additionally, a number of features of these polynomials are established, including symmetric identities, implicit summation formulae, differential equations, series definition and operational formalism.
Rabab Alyusof
semanticscholar   +3 more sources

Monomiality principle, Sheffer-type polynomials and the normal ordering problem [PDF]

Journal of Physics: Conference Series, 2006
We solve the boson normal ordering problem for $(q(a^ )a+v(a^ ))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^ $ are boson annihilation and creation operators, satisfying $[a,a^ ]=1$. This consequently provides the solution for the exponential $e^{ (q(a^ )a+v(a^ ))}$ generalizing the shift operator.
Penson, K.A., Blasiak, P., Dattoli, G., Duchamp, G.H.E., Horzela, A., Solomon, A.I.   +5 more
semanticscholar   +7 more sources

General-Appell Polynomials within the Context of Monomiality Principle [PDF]

International Journal of Analysis, 2013
A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established.
Khan, Subuhi, Raza, Nusrat
semanticscholar   +5 more sources

The Monomiality Principle Applied to Extensions of Apostol-Type Hermite Polynomials

European Journal of Pure and Applied Mathematics
In this research paper, we present a  class of polynomials referred to as Apostol-type Hermite-Bernoulli/Euler polynomials   $\mathcal{U}_\nu(x,y;\rho;\mu)$, which can be given by the following generating function\begin{equation*} \displaystyle \frac{2-\mu+\frac{\mu}{2}\xi}{\rho e^{\xi}+(1-\mu)}e^{x \xi+y \xi^2} =\displaystyle\sum\limits_{\nu=0 ...
Stiven Díaz, William Ramírez, Clemente Cesarano, Juan Hernández, Escarlin Claribel Perez Rodriguez   +4 more
semanticscholar   +4 more sources

Applying the monomiality principle to the new family of Apostol Hermite Bernoulli-type polynomials [PDF]

Communications in Applied and Industrial Mathematics
Abstract In this article, we introduce a new class of polynomials, known as Apostol Hermite Bernoulli-type polynomials, and explore some of their algebraic properties, including summation formulas and their determinant form. The majority of our results are proven using generating function methods.
Ramírez, William, Cesarano, Clemente
semanticscholar   +3 more sources