Fast multipole method for multidimensional integrals

We give a fast algorithm re, evaluate a class of d-dimensional integrals. A direct numerical evaluation of these integrals costs N-d, where d is the number of variables and N is the number of discrete points of each variable. The algorithm we. present in this Note permits to reduce this cost from N-d to a cost of the order O(N). This recursive algorithm takes its inspiration from the well-known Fast-Multipole method. At the end of this paper we give some physical applications of such an algorithm.