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International Mathematics Research Notices 9 (2005) 551--585
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Bessel functions for root systems via the trigonometric setting
Salem Ben Said1, Bent Orsted2

By taking an appropriate limit, we obtain the Bessel functions related to root systems as limit of Heckman-Opdam hypergeometric functions . A more general class of Bessel functions is also investigated, which we shall call the \Theta-Bessel functions. Explicit formuals for the \Theta-Bessel functions are obtained when the multiplicity functions are even and positive integer-valued. This class encloses the Bessel functions on the tangent space at the origin of non-compact causal symmetric spaces, were an integral representation for these special functions is shown.
1:  IECN - Institut Elie Cartan Nancy
2:  Aarhus University [Aarhus]