On Integral Functions of Finite Order Bounded at a Sequence of Points

Let f(z) be an integral function and M(r) = max |f(z)|. The order p of the function is defined by

p=lim log logM(r)/logr.

If p is finite, the upper type k and the lower type l are defined by

l=lim logM(r)/r^r ≤ lim logM(r)/r^p=k.

The function is said to be of maximal, normal or minimal type according as k=∞, a finite positive number or zero.