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arXiv · 0812.0739

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

Margit Rösler·Michael Voit
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Abstract

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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Margit Rösler, Michael Voit. 2008-12-03. A Limit Relation for Dunkl-Bessel Functions of Type A and B. https://doi.org/10.3842/sigma.2008.083

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