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

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Authors

  • Madras University ,IN

DOI:

https://doi.org/10.18311/jims/1937/17323

Abstract

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)/rr ≤ lim logM(r)/rp=k.

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