逐项积分

本文进一步研究了函数项级数的逐项积分定理。

In this paper , the theorems of term-by-term integration have been studied further .

有限区间上广义可积函数列逐项积分的条件

Conditions of Term by Term Integration Sequence of Integrable functions on Finite Interval

本文证明了在一致可积的条件下可对Henstock可积函数列逐项积分；

This paper proves that under the condition on uniformly integrability the sequence of real & valued functions may be integrated term by term .

其次，将逐项积分结果求和并证明了求和结果与传统直接积分法的塑性功率表达式相同；

Then , sum of the termwise integrated results is proved to be equal to that obtained from traditional immediate integration for plastic deformation power .

首先将有鼓形圆盘锻造等效应变速率表示成二维应变速率矢量，对该矢量的内积进行了逐项积分；

First , effective strain rate for disk forging with bulge is expressed in terms of two-dimensional strain rate vector and its inner-product term by term integrated .

利用无穷级数可以将一些复杂的代数函数和超越函数展成简单形式，然后对其进行逐项微分或积分，进而对这些函数处理起来得心应手。

It makes a lot of complex algebraic functions and excessive functions become simple , and then we can differentiate or integrate term by term . Therefore , these functions can be done with easily .

通过具体例子，介绍了幂级数求和的若干种方法：定义法、分项组合法、逐项求导与逐项积分法、代数方程法、微分方程法、升幂除法等。

Through the interpretations of the specific examples , several methods of obtaining the summation function of power series are presented .

文章把连续性和逐项可积性推广到幂级数的收敛域上，并给出幂级数逐项求导与逐项积分后得到的幂级数与原幂级数收敛域之间的关系。

The article extends the continuity and item-by-item to the interval of convergence of power series , and presents the relation between from the item-by-item derivation and term by term integration from power series and the interval of convergence of original power series .