SIGMA 4 (2008), 083, 9 pages      arXiv:0812.0739      https://doi.org/10.3842/SIGMA.2008.083
Contribution to the Special Issue on Dunkl Operators and Related Topics

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

Margit Rösler ^a and Michael Voit ^b
a) Institut für Mathematik, TU Clausthal, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany
^b) Fachbereich Mathematik, TU Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany

Received October 21, 2008, in final form November 26, 2008; Published online December 03, 2008

Abstract
We prove a limit relation for the Dunkl-Bessel function of type B_N with multiplicity parameters k₁ on the roots ±e_i and k₂ on ±e_i±e_j where k₁ 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 k₂. For certain values of k₂ an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.

Key words: Bessel functions; Dunkl operators; asymptotics.

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