On Bessel distributions for quasi-split groups

We show that the Bessel distribution attached by Gelfand and Kazhdan and by Shalika to a generic representation of a quasi-split reductive group over a local field is given by a function when it is restricted to the open Bruh at cell. As in the case of the character distribution, this function is rea l analytic for archimedean fields and locally constant for non-archimidean fields.