Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals

Lee, P.A. (1980) Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals. International Journal of Mathematics and Mathematical Sciences, 3 (4). pp. 761-771. ISSN 0161-1712, DOI https://doi.org/10.1155/S0161171280000555.

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Abstract

Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials {λn(k)(x)} which are defined by the generating function ∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−z)12(x+k),   |z|<1. These polynomials satisfy the orthogonality condition ∫−∞∞pk(x)λm(k)(ix)λn(k)(ix)dx=(−1)nn!(k)nδm,n,   i=−1 with respect to the weight function p1(x)=sech πx pk(x)=∫−∞∞…∫−∞∞sech πx1sech πx2 … sech π(x−x1−…−xk−1)dx1dx2…dxk−1,   k=2,3,…

Item Type:	Article
Funders:	UNSPECIFIED
Uncontrolled Keywords:	Meixner-Pollaczek polynomials; Orthogonal polynomials; Bilinear summation formula; Bivariate distribution; Canonical expansion; Runge identity; G-functions
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Institute of Mathematical Sciences
Depositing User:	Ms. Juhaida Abd Rahim
Date Deposited:	07 Jul 2017 02:29
Last Modified:	07 Jul 2017 02:29
URI:	http://eprints.um.edu.my/id/eprint/17452

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