منابع مشابه
Properties of the Exceptional (X`) Laguerre and Jacobi Polynomials
We present various results on the properties of the four infinite sets of the exceptional X` polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414–417; Phys. Lett. B 684 (2010), 173–176]. These X` polynomials are global solutions of second order Fuchsian differential equations with ` + 3 regular singularities and their confluent limits. We derive equivalent but much...
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Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field K that induce planar functions on infinitely many extensions of K; we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial...
متن کاملThe electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation
We examine the electrostatic properties of exceptional and regular zeros of Xm-Laguerre and Xm-Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, we can deduce an Egerváry-Turán type result as well. The limit of the energy on the regular zeros is also investigated.
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One of the interesting features in the development of analysis in the twentieth century is the remarkable growth, in various directions, of the theory of orthogonal functions. Two brilliant achievements on the threshold of this century—Fejér's paper on Fourier series and Fredholm's papers on integral equations—have been acting as a powerful inspiring source of attraction, inviting analysts to d...
متن کاملLaguerre and Jacobi polynomials
We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials wi...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2019
ISSN: 0021-9045
DOI: 10.1016/j.jat.2018.11.002