关键词: 整函数, 调和整映射, 级, 型

Abstract: In order to discuss the growth estimates of harmonic entire mappings, the order and the type of harmonic entire mappings are studied, and they can be characterized by the coefficients of the analytic parts and anti-analytic parts. For a strictly increasing sequence of positive integers{n_k}^∞_k=1, two quantities are defined by using the values of n_k order derivative of the analytic part and anti-analytic part of a harmonic entire mapping at a certain point, and it is proved that these two quantities are equal to the order and the type of the harmonic entire mapping, respectively, almost everywhere.

Key words: entire function, harmonic entire mapping, order, type