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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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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Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle [PDF]
Applied Mathematics and Computation, 2014 24 pages. 1 figure.
Nelson Faustino
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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 $e^{λ(q(a^†)a+v(a^†))}$ generalizing the shift operator.
K A Penson +2 more
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Monomiality principle, operational methods and family of Laguerre–Sheffer polynomials
Journal of Mathematical Analysis and Applications, 2012 The authors use the monomiality principle formalism and operational methods in order to introduce the Laguerre-Sheffer polynomials. The generating function for these polynomials is derived and a correspondence between the Laguerre-Sheffer and the Sheffer polynomials is established.
Subuhi Khan, Nusrat Raza
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Quasi-Monomiality Principle and Certain Properties of Degenerate Hybrid Special Polynomials
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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Mathematical and Computer Modelling, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M Migliorati, H M Srivastava
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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
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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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A determinantal approach to Sheffer–Appell polynomials via monomiality principle
Journal of Mathematical Analysis and Applications, 2015 The authors have combined the Appell and Sheffer polynomials to introduce Sheffer-Appell polynomials by means of generating function, series definition and determinantal definition. Since any sequence of polynomials is quasi-monomial [\textit{Y. Ben Cheikh}, Appl. Math. Comput. 141, No. 1, 63--76 (2003; Zbl 1041.33008)], the quasi-monomiality operators
Subuhi Khan, Mumtaz Riyasat
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