On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy–Riemann system in Rn+1

In this paper we establish an explicit relation between the growth of the maximum modulus and the Taylor coefficients of the entire solutions to the higher-dimensional Cauchy–Riemann system in Rn+1. This allows us to determine the exact value for the growth order of the maximum modulus for all entire monogenic functions without knowing the precise value for the maximum modulus. Furthermore, it enables us to construct easily examples of entire monogenic functions that exhibit growth behavior of order ρ for any real value 0 ρ ∞. © 2006 Elsevier Inc. All rights reserved.