The theory of polynomial bases in one complex variable, as given by Whittaker and Cannon, was extended partially to the scope of Clifford analysis, where many results have been handled from different aspects. The emphasis of this paper is on introducing a certain type of bases of axially monogenic polynomials generated by the maximum modulus base. Determining the convergence properties of such bases is closely related to the growth behavior of the associated entire axially monogenic functions. We start by investigating the presented bases of monogenic polynomials associated with entire axially monogenic functions in the way we are going to indicate. Then, we show how this leads us to certain relations involving maximum moduli of an entire axially monogenic function on a sequence of balls with increasing radii. In this concern, we point out that Hadamard’s three hyper-balls theorem can be employed to justify some of our results. The significance of this study is due to the variety of the results, which are not normally expected.

Whittaker和Cannon给出的一个复变量的多项式基理论在一定程度上扩展到了Clifford分析的范围，该分析从不同方面处理了许多结果。本文的重点是介绍由最大模数基生成的轴向单基因多项式的某些类型的基。确定此类碱基的收敛特性与关联的整个轴向单基因功能的生长行为密切相关。我们首先以要指出的方式研究与整个轴向单基因功能相关的单基因多项式的基础。然后，我们显示这如何导致我们得出某些关系，其中涉及半径增加的球序列上的整个轴向单基因函数的最大模量。在这方面，我们指出，哈达玛的三个超球定理可以用来证明我们的一些结果是正确的。这项研究的意义在于结果的多样性，而这通常是无法预期的。