Results 41 to 50 of about 490,089 (251)
Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials
, 2015 The bilinear generating function for products of two Laguerre 2D polynomials Lm;n(z; z0) with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials.
Wünsche, Alfred
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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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SymmetryIn the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism.
Mohammed Fadel, Nusrat Raza, Wei-Shih Du
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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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On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials [PDF]
, 2012 Using special technique of expanding ratio of densities in an infinite series of polynomials orthogonal with respect to one of the densities, we obtain simple, closed forms of certain kernels built of the so called Al-Salam-Chihara (ASC) polynomials.
Bożejko M. +2 more
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Fourier transform of hn(x + p)hn(x − p)
International Journal of Mathematics and Mathematical Sciences, 1997 We evaluate Fourier transform of a function with Hermite polynomials involved. An elementary proof is based on a combinatorial formula for Hermite polynomials.
Mourad E. H. Ismail, Krzystztof Stempak
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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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, 2012 We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we
Adler S. L. +4 more
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Mathematics, 2018 In this paper, we study differential equations arising from the generating functions of Hermit Kamp e ´ de F e ´ riet polynomials. Use this differential equation to give explicit identities for Hermite Kamp e ´ de F
Cheon Seoung Ryoo
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A model for the continuous q-ultraspherical polynomials
, 1995 We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q ...
Askey R. A. +4 more
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