关于数列的收敛指数

摘要

G.Pólya给出了收敛指数的定义及计算公式，但没给出证明，现有文献也很难找到其证明.本文给出它的证明，此外，本文还讨论了收敛指数与上指数密度之间的关系，并且给出了一些应用的例子.%The definition of the exponent of convergence and formula of computation are introduced in G.Pólya, but it is difficult to find the proof of the formula in the literature. In this paper, we will give the proof of the formula. In addition, we also discuss the relationship between the exponent of convergence and the upper exponential density. Moreover, we give some examples to illustrate our results.