论文标题
参数欧拉的谐波数量
Parametric Euler Sums of Harmonic Numbers
论文作者
论文摘要
我们定义了广义Euler总和的参数变体和构造轮廓集成，以对这些参数EULER总和进行一些明确的评估。特别是，我们建立了（Hurwitz）Zeta函数，线性和二次参数Euler总和的几个明确公式。此外，我们还通过使用参数Euler和对交替的Riemann Zeta值的组合进行了对交替的双Zeta值$ \ ze（\ overline {2J}，2M+1）$的明确评估。
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions, linear and quadratic parametric Euler sums. Furthermore, we also give an explicit evaluation of alternating double zeta values $\ze(\overline{2j},2m+1)$ in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.
