论文标题
Dirichlet类型Euler总和的扩展
Dirichlet type extensions of Euler sums
论文作者
论文摘要
在本文中，我们研究了交替的Euler $ t $ - sums和$§$ -SUMS，它们是无限级数，涉及（交替的）奇数谐波数，并且与Dirichlet Beta函数具有相似的形式和密切的关系。通过使用残留计算方法，我们为（交替的）线性和二次Euler $ t $ sums和$§$ sums建立了明确的公式，从中，霍夫曼（Hoffman）的双倍和三重$ t $ values和kaneko-tsumura的双重和tsumura的双重和三重$ t $ t $ t $ t $ t $ t $ -value均可享受霍夫曼（Hoffman）的平价定理。作为补充剂，我们还表明，线性$ t $ - sums和$§$ -Sums可以用彩色的多个Zeta值表示。提出了一些有趣的后果和说明性的例子。
In this paper, we study the alternating Euler $T$-sums and $§$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of residue computations, we establish the explicit formulas for the (alternating) linear and quadratic Euler $T$-sums and $§$-sums, from which, the parity theorems of Hoffman's double and triple $t$-values and Kaneko-Tsumura's double and triple $T$-values are further obtained. As supplements, we also show that the linear $T$-sums and $§$-sums are expressible in terms of colored multiple zeta values. Some interesting consequences and illustrative examples are presented.
