  Analysis of function spaces and special functions are closely related to the
representation theory of Lie groups. We explain here the connection between the
Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck
polynomials on the one side, and highest weight representations of Hermitian
Lie groups on the other side. The representation theory is used to derive
differential equations and recursion relations satisfied by those special
functions.
