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

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

2008-12-03

arxiv.org/abs/0812.0739v1

SIGMA 4 (2008), 083, 9 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Scientific paper

10.3842/SIGMA.2008.083

We prove a limit relation for the Dunkl-Bessel function of type $B_N$ with multiplicity parameters $k_1$ on the roots $\pm e_i$ and $k_2$ on $\pm e_i\pm e_j$ 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.

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