p级数的求和

通过积分转移、余项逼近的方法,建立起一系列p级数的求和公式,并给出了便于操作的误差估计方法.一改把级数余项当作误差来估计的传统做法,而是将余项作为和的重要组成部分进行分析,使得每增加一项计算量,精度能提升二个以上指数级,从而有效地解决了p级数的求和问题.

The Sum of p-series

We set up a series of sum formulas of p-series through the integral transference & the remainder approximation method, and give a convenience method of error estimation. We take the remainder be as the important component of the sum to analysis instead of take the remainder be as error to estimate in the traditional method, so the precision could be raised more than two exponential orders when add one term in calculation, so we solved the problem of sum of p-series efficiently.