1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity

1.1

in which D 2 = d 2/du 2. Furthermore, when g is a solution of y″ + λ 2 y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to

1.2

In this note we generalize these results to the real Euclidean space EN , our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of

1.3

to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.