The Extended Dunkl Oscillator and the Generalized Hermite Polynomials on the Radial Lines
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DOI: 10.1007/s44198-024-00224-x
Abstract: Model of the extended Dunkl oscillator based on Milovanović generalized Hermite polynomials on radial rays is discussed. Simple explicit realization of creation and annihilation operators in terms of difference-differential operators, coherent states are investigated. read more here.
Keywords: dunkl oscillator; extended dunkl; generalized hermite; hermite polynomials ... See more keywords
Quantum algebra from generalized q-Hermite polynomials
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DOI: 10.1016/j.jmaa.2019.07.047
Abstract: Abstract In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomials h ˜ n , α ( x ; q ) , introduced by Mezlini et al. in 2014. Our… read more here.
Keywords: quantum algebra; algebra generalized; hermite polynomials; generalized hermite ... See more keywords
Generating functions for generalized Hermite polynomials associated with parabolic cylinder functions
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DOI: 10.1080/10652469.2019.1697695
Abstract: ABSTRACT In this article, we first give some basic properties of generalized Hermite polynomials associated with parabolic cylinder functions. We next use Weisnerś group theoretic method and operational rules method to establish new generating functions… read more here.
Keywords: generalized hermite; associated parabolic; generating functions; hermite polynomials ... See more keywords
Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials
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DOI: 10.1093/imrn/rny172
Abstract: The Painlevé-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers $m$ and $n$. These functions have applications to nonlinear wave equations, random… read more here.
Keywords: rational painlev; generalized hermite; functions associated; hermite polynomials ... See more keywords
New estimates on generalized Hermite–Hadamard–Mercer-type inequalities
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DOI: 10.1186/s13661-025-02012-y
Abstract: The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality. This inequality, which is derived through the… read more here.
Keywords: mercer; inequality; generalized hermite; hermite hadamard ... See more keywords
On Spectral Vectorial Differential Equation of Generalized Hermite Polynomials
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DOI: 10.3390/axioms11070344
Abstract: In this paper, we first give some results on monic generalized Hermite polynomials (GHP) {Hn(μ)(x)}n≥0, orthogonal with respect to the positive weight |x|2μe−x2,μ>−12,x∈R, which will lead to the formulation of the second-order spectralvectorial differential equation… read more here.
Keywords: equation; spectral vectorial; differential equation; hermite polynomials ... See more keywords
On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals
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DOI: 10.3390/sym12040595
Abstract: Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of… read more here.
Keywords: generalized hermite; tempered fractional; fractional integrals; hadamard inequalities ... See more keywords
A New Class of Laguerre-Based Generalized Hermite-Euler Polynomials and its Properties
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DOI: 10.46793/kgjmat2001.089k
Abstract: The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of partial differential equations often encountered in physical problems. Motivated by their importance and potential… read more here.
Keywords: euler; generalized hermite; based generalized; euler polynomials ... See more keywords