A Generalization of Euler's Theorem for zeta(2k)

作者：Murty M Ram^*; Weatherby Chester^*

来源：American Mathematical Monthly, 2016, 123(1): 53-65.

DOI：10.4169/amer.math.monthly.123.1.53

We extend Euler's celebrated theorem evaluating zeta(2k). We replace the terms n(-2k) in the infinite sum for zeta(2k), with (n(2) + Bn + C)(-k) where B, C are complex and k is a positive integer. We explicitly evaluate these sums and also briefly discuss their transcendence.

• 出版日期2016-1