Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

E. K. Narayanan, A. Pasquale, S. Pusti

A series expansion for Heckman-Opdam hypergeometric functions ${\phi }_{\lambda }$ is obtained for all $\lambda \in {\mathfrak{a}}_{\mathbb{C}}^{\ast }.$ As a consequence, estimates for ${\phi }_{\lambda }$ away from the walls…