Results 51 to 60 of about 525,666 (282)
Roots of generalised Hermite polynomials when both parameters are large [PDF]
, 2019 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 region, and organise themselves on a ...
D. Masoero, Pieter Roffelsen
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A characterization of Hermite polynomials
Journal of Computational and Applied Mathematics, 1997 AbstractWe show that for any orthogonal polynomials Pn(x)n=0∞ satisfying a spectral type differential equation of order N (⩾2) essentially Hermite polynomials if and only if the leading coefficient lN(x) is a nonzero constant.
Kwon, KH Kwon, Kil Hyun +2 more
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Some Integrals Involving q-Laguerre Polynomials and Applications
Abstract and Applied Analysis, 2013 The integrals involving multivariate q-Laguerre polynomials and then auxiliary ones are studied. In addition, the representations of q-Hermite polynomials by q-Laguerre polynomials and their related integrals are given.
Jian Cao
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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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Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials [PDF]
International mathematics research notices, 2017 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 $n$.
R. Buckingham
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Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials
Mathematics, 2018 The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition.
Subuhi Khan, Tabinda Nahid
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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Durfee Rectangles and Pseudo‐Wronskian Equivalences for Hermite Polynomials [PDF]
Studies in applied mathematics (Cambridge), 2016 We derive identities between determinants whose entries are Hermite polynomials. These identities have a combinatorial interpretation in terms of Maya diagrams, partitions and Durfee rectangles, and serve to characterize an equivalence class of rational ...
D. Gómez‐Ullate +2 more
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Fractional Supersymmetric Hermite Polynomials [PDF]
Mathematics, 2020 We provide a realization of fractional supersymmetry quantum mechanics of order r, where the Hamiltonian and the supercharges involve the fractional Dunkl transform as a Klein type operator. We construct several classes of functions satisfying certain orthogonality relations.
Fethi Bouzeffour, Wissem Jedidi
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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