ζ(i)的一个新的卷积公式(英文)

A New Convolution Formula of ζ(i)

本文利用概率方法讨论了关于Riemann Zeta函数ζ(i)的卷积∑k-2 i=2ζ(k-i),k≥4, Euler证明了这个卷积与级数∑n≥1 Hn/nk-1有关,使用Stirling展开我们发现了一个新的不同的结果．

The convolution of Riemann-zeta function ∑^k-2 i=2 ∑（k-i）,k≥4 is discussed applying the probabilistic methods in this paper, a new evaluation formula of series involving the partial sums ξn（τ）,different from Euler＇s result of the series ∑ n≥1 Hn/n^（k-1）, is established by Stirling expansion.