N.H.Abel定理的推广

Generalization of N.H.Abel′s Theorem

本文详尽讨论了级数∑nanSnαSn-1β(α,β0)的敛散性.式中Sn=∑nk=1ak(ak0)→+∞(n→∞)从中得到一些有价值的结果.N.H.Abel定理则是文中命题2(当β=0,α=1+ρ,ρ>0时)之特例.

This paper discusses the convergence and divergence of series (α,β0),where Sn=(ak0)→+∞(n→∞) and obtains and series of valuable results.N.H.Abel′s theorem is a example of the proposition 2 in the paper.