منابع مشابه
Szegö on Jacobi Polynomials
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...
متن کاملCariñena Orthogonal Polynomials Are Jacobi Polynomials
The relativistic Hermite polynomials (RHP) were introduced in 1991 by Aldaya et al. [3] in a generalization of the theory of the quantum harmonic oscillator to the relativistic context. These polynomials were later related to the more classical Gegenbauer (or more generally Jacobi) polynomials in a study by Nagel [4]. For this reason, they do not deserve any special study since their properties...
متن کاملA class of matrix-valued polynomials generalizing Jacobi polynomials
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations. 1. Motivation The understanding of matrix-valued orthogonal polynomi...
متن کاملA Family of Generalized Jacobi Polynomials
The family of orthogonal polynomials corresponding to a generalized Jacobi weight function was considered by Wheeler and Gautschi who derived recurrence relations, both for the related Chebyshev moments and for the associated orthogonal polynomials. We obtain an explicit representation of these polynomials, from which the recurrence relation can be derived.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1977
ISSN: 0022-247X
DOI: 10.1016/0022-247x(77)90058-0