  This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg.
Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach
to examine the action of a group on a curve within a generalization of jet
space known as multispace. Here we seek to further study group actions on the
multispace of curves by computing the infinitesimals for a given action. For
the most part, we proceed formally, and produce in the multispace a recursion
relation that closely mimics the previously known prolongation recursion
relations for infinitesimals of a group action on jet space.
