Lee, P.A. (1980) Probabilistic derivation of a bilinear summation formula for the MeixnerPollaczek polynominals. International Journal of Mathematics and Mathematical Sciences, 3 (4). pp. 761771. ISSN 01611712, DOI https://doi.org/10.1155/S0161171280000555.

PDF (Full Text)
LeePA_(1980).pdf  Published Version Download (2MB) 
Abstract
Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the MeixnerPollaczek 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:  MeixnerPollaczek polynomials; Orthogonal polynomials; Bilinear summation formula; Bivariate distribution; Canonical expansion; Runge identity; Gfunctions 
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 
Actions (login required)
View Item 