Growth of entire harmonic functions in [R.sup.n], n [greater than or equal to] 2

Let h be a harmonic function on Rn, n [greater than or equal to] 2. Then there exists on entire function f on C such that f(u) = h(u, 0, ..., 0) for all real u. This fact has been used to deduce theorems for harmonic function on [R.sup.n] from classical results about entire functions. Moreover, we have considered the characterizations of lower order and lower type of h in terms of coefficients and ratio of these successive coefficients occurring in power series expansion off. Keywords and Phrases: Homogeneous harmonic polynomials, Entire harmonic function, Laplace's equation, Lower order and lower type.
1. Introduction A twice differentiable function h(x), x = ([x.sub.1], [x.sub.2], ..., [x.sub.n]); which is a solution of Laplace's equation [[[[partial derivative].sup.2]h]/[[partial derivative][x.sub.1.sup.2]]] + [[[[partial derivative].sup.2]h]/[[partial derivative][x.sub.2.sup.2]]] + ... + [...]