On contractions of hypergeometric functions associated with root systems

In this paper we extend previous classes of generalized Bessel functions. This follows via a limit transition from Heckman-Opdam's results in the theory of hypergeometric functions. Our starting point is to obtain the Bessel functions associated with Cartan motion groups by means of Harish-Chandra's spherical functions. Bessel functions related to noncompact causal symmetric spaces are also investigated. This paper is a survey of recent results in [BO1] and [BO2].