The Dunkl-Laplace transform and Macdonald’s hypergeometric series

We continue a program generalizing classical results from the analysis on symmetric cones to Dunkl setting for root systems of type A A . In particular, we prove Dunkl-Laplace transform identity Heckman-Opdam hypergeometric functions and more generally, associated Opdam-Cherednik kernel. This is achieved by analytic continuation Laplace non-symmetric Jack polynomials which was stated, case, as key conjecture I.G. Macdonald [arXiv:1309.4568v1]. Our proof based operator techniques raising Knop Sahi. Moreover, use these establish identities between series in terms polynomials. Finally, conclude with Post-Widder inversion formula transform.