关于超球级数所定义的整函数

On the Entire Function Defined by Hyperspherical Series

给出了超球级数所定义的整函数的下阶、下型与极大项、中心指标、最大模之间的关系及几个不等式,并由此推出了超球级数成正规增长的充要条件及成完全正规增长的充要条件.

In this paper, some inequalities are found among M（a）｜f（cosh（a＋bi）） ｜, b∈[0, 2π], maximal term μ（a） and central norm v（α）. Moreover, we obtain the sufficient and necessary conditions for f（z） = ∞∑n=0 CnPn^（α,α） （Z） to be regularly grown and completely regularly grown.