慢收敛级数的求和

运用递推方法，得到了任意阶的积分转移公式，并构造出具有差分形式的积分展开公式，由此建立起以融人余项构成为特征的级数求和公式，实现了对求和误差的控制，对于收敛速度很慢的级数，只需计算10余项之和，就能达到十位精度，有效地解决了慢收敛级数的求和问题，通过对误差估计的深入讨论，定量地给出了提高求和精度的途径，同时指出了求和公式的渐近性质。

Summation of Slowly Convergent Series

Using the recurrence method, we obtain the integral transference formula of arbitrary order, construct a integral expansion formula with the difference form, and from this, we set up a sum formula of the series which has the characteristic that the remainder term retained in the formula and can to realize the error control of the summation. For the slowly convergent series, we can obtain precision to ten digits with ten and a few more teams also of the series. Thus we solve the summation problem of slowly convergent series efficiently. And then, we also give a way to improve the precision of the summation quantitatively through detailed analysis of the error estimate, and point out the asymptotic properties of the formula.