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On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties
AxiomsIn this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence ...
Ahmed Bakhet +4 more
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Turán inequalities for symmetric orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, 1997 A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials ...
Joaquin Bustoz, Mourad E. H. Ismail
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Mathematics, 2021 Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem.
Mohammad Izadi +2 more
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Mehler-Heine asymptotics for multiple orthogonal polynomials
, 2016 Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
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A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian [PDF]
, 2014 We consider compact Grassmann manifolds $G/K$ over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type $BC$.
Rösler, Margit, Voit, Michael
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On the zeros of generalized Bessel polynomials. I
Indagationes Mathematicae (Proceedings), 1981 AbstractIn this paper, the location of the zeros of generalized Bessel polynomials is studied, leading to many improvements of previous results.
Edward B. Saff +2 more
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q-Bessel functions: the point of view of the generating function method [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1997 We show that the generating function method allows a fairly straightforward understanding of the properties of q-Bessel functions. We analyze three different forms of cylindrical q-Bessel functions so far proposed, discuss their generating functions, the
G. Dattoli, A. Torre
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Finite Integral Formulas Involving Multivariable Aleph-Functions
Journal of Applied Mathematics, 2019 The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials.
Hagos Tadesse +2 more
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From Circular to Bessel Functions: A Transition through the Umbral Method
Fractal and Fractional, 2017 A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions.
Giuseppe Dattoli +3 more
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Zeros of Ramanujan Type Entire Functions
, 2016 In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials $L_{n}^{(\alpha)}(x;q)$, while the entire functions are generalizations of Ramanujan's entire function $A_{q}(z)$, q-
Zhang, Ruiming
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