论文标题
koecher关于Riemann Zeta功能的Markov-apéry类型公式
On a result of Koecher concerning Markov-Apéry type formulas for the Riemann zeta function
论文作者
论文摘要
Koecher在1980年得出了一种在奇数正整数处获得Riemann Zeta函数身份的方法，其中包括由于Markov而导致的$ζ（3）$的经典结果，并由Apéry重新发现。在本文中，我们将Koecher的方法扩展到非常通用的环境，并证明了两个更具体但仍然相当一般的结果。作为应用，我们获得了交替的Euler总和，Markov-apéry类型身份以及$π$的权力的身份的无限类别的身份
Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for $ζ(3)$ due to Markov and rediscovered by Apéry. In this paper we extend Koecher's method to a very general setting and prove two more specific but still rather general results. As applications we obtain infinite classes of identities for alternating Euler sums, further Markov-Apéry type identities, and identities for even powers of $π$
