Document Type
Article
Publication Date
1-1-1980
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,…
Keywords
Meixner-Pollaczek polynomials, Orthogonal polynomials, Bilinear summation formula, Bivariate distribution, Canonical expansion, Runge identity, G-functions
Divisions
MathematicalSciences
Publication Title
International Journal of Mathematics and Mathematical Sciences
Volume
3
Issue
4
Publisher
Hindawi Publishing Corporation