On the Average Radial Increase of a Certain Class of Integral Functions of Order One and Finite Type

Let z = re^iθ = x + iy. We write R(z) = x, I(z) = y. Let f(z) be an integral function and

M (r,f) = max|f(z)|.

We shall say that f(z) is of order one and finite type when

lim log M(r, f)/r < ∞.                                               (1)