منابع مشابه
On Co-recursive Orthogonal Polynomials
is equivalent to (1.1) with 6„ = 0 (w^2) and Pi(0)p^0. The condition b„ = 0 (w^2) suggests the symmetric case, (i.e.,P„( — x) = ( —l)"P„(x)) but this is denied by the condition Pi(0) ^0. (In fact, (1.2) shows that Pn( — r)^0 whenever Pn(r)=0.) It then seems natural to ask what relations exist between a set of polynomials satisfying (1.2) and the corresponding symmetric polynomials which would b...
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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...
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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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Given a suitable weight on IR, there exist many (recursive) three term recurrence relations for the corresponding multivariate orthogonal polynomials. In principle, these can be obtained by calculating pseudoinverses of a sequence of matrices. Here we give an explicit recursive three term recurrence for the multivariate Jacobi polynomials on a simplex. This formula was obtained by seeking the b...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(93)e0246-i