  Let H be a split reductive group over a local non-archimedean field, and let
H^ denote its Langlands dual group. We present an explicit formula for the
generating function of an unramified L-function associated to a highest weight
representation of the dual group, considered as a series of elements in the
Hecke algebra of H. This offers an alternative approach to a solution of the
same problem by Wen-Wei Li. Moreover, we generalize the notion of "Satake
transform" and perform the analogous calculation for a large class of spherical
varieties.
