Results 31 to 40 of about 33,296 (252)
Appell and Sheffer sequences: on their characterizations through functionals and examples
Comptes Rendus. Mathématique, 2021 The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature ...
Carrillo, Sergio A., Hurtado, Miguel
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On peculiar properties of generating functions of some orthogonal polynomials [PDF]
, 2012 We prove that for |x|,|t|
Szabłowski, Paweł J.
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On a Generalisation of Hermite Polynomials [PDF]
Proceedings of the American Mathematical Society, 1971 In this paper, the author introduces a generalisation of the Hermite polynomials. Hypergeometric representations, a new generating relation and n n th order differential formulae for the generalised polynomials have also been derived therein.
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Zeros of exceptional Hermite polynomials [PDF]
Journal of Approximation Theory, 2015 We study the zeros of exceptional Hermite polynomials associated with an even partition $λ$. We prove several conjectures regarding the asymptotic behavior of both the regular (real) and the exceptional (complex) zeros. The real zeros are distributed as the zeros of usual Hermite polynomials and, after contracting by a factor $\sqrt{2n}$, we prove that
Robert Milson, Arno B. J. Kuijlaars
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials [PDF]
, 2013 We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic ...
Gomez-Ullate, David +2 more
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A characterization of Hermite polynomials
Journal of Computational and Applied Mathematics, 1997 The authors consider a spectral type linear differential equation with polynomial coefficients of order \(N(\geq 1)\), namely: \[ L_N[y](x)= \sum_{i=1}^N \sum_{j=0}^i \ell_{ij}x^jy^{(i)}(x)= \lambda_ny(x), \tag{\(*\)} \] where \(\ell_{ij}\) are given constants while \[ \lambda_n= n\ell_{11 ...
Kwon, KH Kwon, Kil Hyun +2 more
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Hermite polynomials and Fibonacci oscillators [PDF]
Journal of Mathematical Physics, 2019 We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states.
Francisco A. Brito +2 more
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Series Prediction based on Algebraic Approximants [PDF]
, 2011 It is described how the Hermite-Pad\'e polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Pad\'e polynomials.
Homeier, Herbert H. H.
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Vortices and Polynomials [PDF]
, 2009 The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical vortices on the
Ablowitz +53 more
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A $q$-deformation of true-polyanalytic Bargmann transforms when $q^{-1}>1$
Comptes Rendus. Mathématique, 2022 We combine continuous $q^{-1}$-Hermite Askey polynomials with new $2D$ orthogonal polynomials introduced by Ismail and Zhang as $q$-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer ...
El Moize, Othmane, Mouayn, Zouhaïr
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