论文标题
Euler类型总和的扩展名和Ramanujan类型总和
Extensions of Euler Type Sums and Ramanujan Type Sums
论文作者
论文摘要
我们定义了一种新型的古典Digamma功能，并建立了一些基本身份。然后，我们应用了获得的公式，并扩展了Flajolet和Salvy开发的工具来研究更通用的Euler型总和。 Flajolet和Salvy的论文\ Cite {FS1998}的主要结果是本文主要结果的直接推论。此外，我们提供了涉及双曲线系列的Ramanujan型身份的一些参数化扩展。考虑了一些有趣的新后果和说明性的例子。
We define a new kind of classical digamma function, and establish its some fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler type sums. The main results of Flajolet and Salvy's paper \cite{FS1998} are the immediate corollaries of main results in this paper. Furthermore, we provide some parameterized extensions of Ramanujan-type identities that involve hyperbolic series. Some interesting new consequences and illustrative examples are considered.
