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多重级数收敛的两种等价定义

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多重级数为级数理论中的一个重要研究对象,在多元函数的微积分学、多复变函数里有着重要的应用.采用类比法,将多重级数分为多重数项级数和函数项级数,分别给出多重数项级数收敛及函数项级数一致收敛的等价定义,且证明了其等价性.
Two Equivalent Definitions for the Convergence of Multiple Series
Multiple series,an important research object in series theory,has significant applications in the calculus of multivariable functions and multi-complex variable functions.The analogy is used to divide multiple series into multiple term series and function term series,and two equivalent definitions for the convergence of multiple series with multiple terms and the uniform convergence of multiple series with multiple function terms are given respectively,and the equivalence is proved.

multiple seriesconvergenceequivalent definition

郭烨、郝珺宇

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湖北师范大学文理学院 理工学部,湖北 黄石 435109

多重级数 收敛 等价定义

2024

南通职业大学学报
南通职业大学

南通职业大学学报

影响因子:0.366
ISSN:1008-5327
年,卷(期):2024.38(4)