A note on integral functions
- 1 July 1932
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 28 (3) , 262-265
- https://doi.org/10.1017/s0305004100010100
Abstract
1. Let f(z) denote an integral function of finite order ρ. We write It has been shown that where hρ is a constant which depends only on ρ. We are naturally led to enquire whether some equation of the form (1.1) may be true with lim sup replaced by lim inf. In this note we show that the reverse is true. We construct an integral function of zero order for which The proof may easily be modified to construct a function of any finite order or of infinite order for which (1.2) is satisfied.This publication has 0 references indexed in Scilit: