Dual addition formulas: the case of continuous q-ultraspherical and q-Hermite polynomials
Sign Up to like & getrecommendations! Published in 2021 at "Ramanujan Journal"
DOI: 10.1007/s11139-021-00426-7
Abstract: We settle the dual addition formula for continuous q-ultraspherical polynomials as an expansion in terms of special q-Racah polynomials for which the constant term is given by the linearization formula for the continuous q-ultraspherical polynomials.… read more here.
Keywords: hermite polynomials; addition; dual addition; continuous ultraspherical ... See more keywords
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
Roots of generalised Hermite polynomials when both parameters are large
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DOI: 10.1088/1361-6544/abdd93
Abstract: We study the roots of the generalised Hermite polynomials H m,n when both m and n are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic… read more here.
Keywords: generalised hermite; parameters large; hermite polynomials; roots generalised ... 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
Determination of Thermal Boundary Conditions using Piecewise Hermite Polynomials during the Air Transfer Step of an Industrial Quenching Process
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DOI: 10.1115/1.4068867
Abstract: The study herein presents the identification of the thermal boundary conditions during the air travel step before quenching by immersion under an industrial environment. The experimental characterization was done with quench probes instrumented with multiple… read more here.
Keywords: hermite polynomials; step; boundary conditions; air transfer ... See more keywords
Polyanalytic Hermite polynomials associated with the elliptic Ginibre model
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DOI: 10.1142/s0129055x25500321
Abstract: Motivated by the connection between the eigenvalues of the complex Ginibre matrix model and the magnetic Laplacian in the complex plane, we derive analogues of the complex Hermite polynomials for the elliptic Ginibre model. To… read more here.
Keywords: ginibre model; hermite polynomials; elliptic ginibre; ginibre ... See more keywords
Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states
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DOI: 10.1142/s0219887820500218
Abstract: We use the recursion relations of the continuous q-Hermite polynomials and obtain the q-difference realizations of the ladder operators of a q-oscillator algebra in terms of the Askey–Wilson operat... read more here.
Keywords: oscillator algebra; approach continuous; hermite polynomials; continuous hermite ... See more keywords
Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
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DOI: 10.1515/gmj-2024-2071
Abstract: Abstract This work presents a general framework that innovates and explores different mathematical aspects associated with special functions by utilizing the mathematical physics-based idea of monomiality. This study presents a unique family of multivariable Hermite… read more here.
Keywords: multivariable hermite; hermite polynomials; genocchi polynomials; frobenius genocchi ... See more keywords
Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials
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DOI: 10.1515/math-2024-0080
Abstract: Abstract This study presents a novel family of bivariate 2D- q q Hermite polynomials. We derive explicit forms and q q -partial differential equations and investigate numerical aspects associated with these polynomials. Furthermore, we deduce… read more here.
Keywords: family bivariate; novel family; hermite polynomials; bivariate hermite ... See more keywords