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

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

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.

Bibliographic Details
Main Author: P. A. Lee
Format: Article
Language:English
Published: Hindawi Limited 1980-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Meixner-Pollaczek polynomials
orthogonal polynomials
bilinear summation formula
bivariate distribution
canonical expansion
Runge identity
G-functions.
Online Access:http://dx.doi.org/10.1155/S0161171280000555

Internet

http://dx.doi.org/10.1155/S0161171280000555

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