A Limit Relation for Dunkl-Bessel Functions of Type A and B

Abstract

We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k_1 on the roots ±ei and k_2 on ±e_i±e_j where k_1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type A_{N−1} with multiplicity k_2. For certain values of k_2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.

Keywords

• Bessel functions
• Dunkl operators
• asymptotics