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
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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
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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
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Two-Variable q-General-Appell Polynomials Within the Context of the Monomiality Principle [PDF]
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
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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
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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
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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
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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.
Subuhi Khan, Nusrat Raza
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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.
K. A. Penson +5 more
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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
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