一致收敛二元函数列及函数项级数的含参量积分性质

doi:10.16039/j.cnki.cn22-1249.2023.01.019

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摘要

通过二元函数列的含参量积分存在性、连续性、可微性及可积性研究了一致收敛的极限函数及函数项级数和函数对应的含参量积分的存在性、连续性、可微性与可积性。获得了一致收敛意义下极限函数对应的含参量积分与极限交换次序、求导交换次序及累次积分交换次序的条件，得到了一致收敛意义下含参量积分与无穷求和交换次序，含参量积分的求导与无穷求和交换次序的条件。

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	费时龙
	任雅柔

关键词: 一致收敛含参量积分二元函数列极限函数函数项级数和函数

Abstract:

In this paper, the existence, the continuity, differentiability and integrability of parametric integrals corresponding to uniformly convergent limit functions and the series of function items are studied through the existence, the continuity, differentiability and integrability of parametric integrals of binary function sequences. We obtain the conditions of the exchange order of parametric integrals about limit function and the limit order, derivative and the cumulative integral in the sence of uniformly convergence. At last, the conditions that exchange order of parametric integrals and infinite sum and derivative are obtained.

Key words: uniform convergence parametric integral sequence of binary functions limit functions series of function items

出版日期: 2023-01-25 发布日期: 2023-01-25 整期出版日期: 2023-01-25

ZTFLH:

O172

引用本文:

费时龙, 任雅柔. 一致收敛二元函数列及函数项级数的含参量积分性质 [J]. 吉林化工学院学报, 2023, 40(1): 95-98.
FEI Shilong, REN Yarou. The Parametric Integral Properties of Limit Functions of Uniformly Convergent Binary Function Sequences and Series of Function Items . Journal of Jilin Institute of Chemical Technology, 2023, 40(1): 95-98.

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http://xuebao.jlict.edu.cn/CN/10.16039/j.cnki.cn22-1249.2023.01.019 或 http://xuebao.jlict.edu.cn/CN/Y2023/V40/I1/95

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