Let (R, m) be a commutative Noetherian local ring the maximal ideal and A an Artinian R-module with Ndim A = d. For each system of parameters x (x1 , ., xd ) of A, we denote by e(x, A) the multipility of A with respect to x. Let n (n1 , n2 , ., nd ) be a d-tuple of positive integers. The paper concerns to the function d-variables I(x(n); A) := where