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

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.

Keywords

• Meixner-Pollaczek polynomials
• orthogonal polynomials
• bilinear summation formula
• bivariate distribution
• canonical expansion
• Runge identity
• G-functions.