一类条件收敛的级数在一类置换下保广义和

A Class of Conditionally Convergent Series Whose Generalized Sums Are Preserved under a Class of Permutations

摘要: 条件收敛级数在重排作用下的求和稳定性分析是经典分析中的一个重要课题。 已有研究主要关注保持所有条件收敛级数的重排以及保持一般意义下的和。本文针对一类交错级数，从渐进密度观点出发引入新的渐进平衡置换类，井证明这一大类交错级数在这类置换下Abel和与Cesaro和均保持不变。

Abstract: The stability of summation values of conditionally convergent series under rearrange- ments is a classical topic in analysis. Existing studies mainly focus on characterizing rearrangements that preserve all conditionally convergent series or that preserve the limit in the ordinary sense. In this paper, we consider a broad class of alternating series and, from the viewpoint of asymptotic density, introduce a new family of asymp- totically balanced permutations. It is shown that for these series, both the Abel sum and the Cesaro sum remain invariant under such rearrangements.