Continuous Hahn functions as Clebsch-Gordan coefficients
Classical Analysis and ODEs
2007-05-23 v1 Representation Theory
Abstract
An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial -hypergeometric functions that we consider as continuous Hahn functions. An integral transform pair with continuous Hahn functions as kernels is also proved. These results have an interpretation for the tensor product decomposition of a positive and a negative discrete series representation of with respect to hyperbolic bases, where the Clebsch-Gordan coefficients are continuous Hahn functions.
Cite
@article{arxiv.math/0302251,
title = {Continuous Hahn functions as Clebsch-Gordan coefficients},
author = {Wolter Groenevelt and Erik Koelink and Hjalmar Rosengren},
journal= {arXiv preprint arXiv:math/0302251},
year = {2007}
}