A Weinstein and L. E. Payne had obtained decomposition formulae for the Solutions of the equation T^ k™ u = O, where Lk n S i=l 32 a xı2 32 + + — y 8 In this paper, we will extend the decomposition formulae for the Solutions of the equation m a2 i=ı SXj2 V i-1 Xi d Xj u = 0. u + d 1. Let us consider the differential operatör a2 5 ax .2 + -«k (1 Xk a X,■k k < n) where e R is an arbitrary constant. Let the function u u (x 2,.- - ■ ,) e be the solution of the eguation ‘n, Li '“k u = 0. X n a Such a solution will be denoted by u {aı^}.