Generating functions for Jacobi and Laguerre polynomials
نویسندگان
چکیده
منابع مشابه
Laguerre 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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Multiplicative renormalization method (MRM) for deriving generating functions of orthogonal polynomials is introduced by Asai–Kubo– Kuo. They and Namli gave complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−κ. In this paper, MRM-factors h(x) for which the beta distribution B(p, q) over [0, 1] is MRM-applicable are determined. In other words, all generating function...
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The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...
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-A well-known generating function of the classical Laguerre polynomials was recently rederived probabillstically by Lee. In this paper, some other (presumably new) generating functions for the Laguerre polynomials are derived by means of probabillstic considerations. A direct (analytical) proof of each of these generating functions is also presented for the sake of completeness. © 1999 Elsevier...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0249694-7