欧拉收敛技术的提炼与广义欧拉常数族的定义

Extracted Euler's Convergence Technique and a Defination on the Generalized Euler' Constant Family

揭示了将调和级数减去对数项以后就能收敛的本质,从这一个案例出发提炼出了一般做法,命名为"欧拉收敛技术".将欧拉收敛技术应用到一大类发散级数上,构造出了新的收敛级数,并且得出与欧拉常数类似的正实数集合,称为"广义欧拉常数族".给出广义欧拉常数族中几个典型的数值算例.

This paper reveals the convergence nature of a logarithm item subtracted from harmonic series. A general method was extracted from this special case to be nominated as the Euler＇s convergence technique. Moreover, the Euler＇s convergence technique in many exhale series is used to construct new convergence series. Then, a set of positive real number is obtained and named as the generalized Euler＇constant family. Finally, typical numerical experiments were given to show the computational results of the generalized Euler＇ constant family.