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=0λn(k)(x)zn/n!=(1+z)12(xk)/(1z)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=1with respect to the weight function p1(x)=sechπxpk(x)=sechπx1sechπx2sechπ(xx1xk1)dx1dx2dxk1,k=2,3,