Results 1 to 10 of about 92 (89)
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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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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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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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
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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.
Khan, Subuhi, Raza, Nusrat
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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
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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
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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
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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.
Penson, K.A. +5 more
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