| 摘要: |
| 通过选取特殊的Kernel函数，探究Euler和之间的递推关系，利用Cauchy-Lindelof引理和Cauchy留数定理，得出了线性Euler和之间存在着与Riemann zeta函数相关的线性递推关系，并进一步证明了在特定条件下，交错Euler和之间的递推关系与交错Zeta函数密切相关，而且这个递推关系仍然是线性的；最后将Euler和的情形进行推广，得到了两个一般和的表达式. |
| 关键词: Euler和 Kernel函数 Cauchy-Lindelof引理 留数 |
| DOI： |
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| The Recurrence Relations of Euler Sums |
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HE Shen dong
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| Abstract: |
| The relationship between different Euler sums is explored by selecting special Kernel functions. We get a linear recurrence relation between different Euler sums by using Cauchy Lindelof lemma and Cquchy residue theorem， which is linked to Riemann zeta function. It is further proved that the recurrence relation between different alternating Euler sums is closely related to alternating zeta function under some special conditions， and this relation is still a linear relation. Finally， two general sums are obtained by generalizing the situation of Euler sums. |
| Key words: Euler sums Kernel function Cauchy Lindelof lemma residues |
