Abstract

Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss’s second summation theorem). Our aim in this paper is to establish a further extension of Gauss’s second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth’s old sum (or the Reed Dawson identity) and (ii) Riordan’s identity in the most general form. A few interesting results are obtained as special cases of our main findings.

中文翻译：

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关于高斯第二求和定理的进一步扩展及其对两个著名组合恒等式扩展的应用的注释

摘要

最近，Masjed-Jamei 和 Koepf 建立了几个经典求和定理（包括高斯第二求和定理）的扩展。我们在本文中的目的是建立对最一般形式的 Masjed-Jamei 和 Koepf 的高斯第二求和公式的进一步扩展。然后将结果应用于获得 (i) Knuth 的旧总和（或 Reed Dawson 恒等式）和 (ii) Riordan 恒等式的最一般形式的扩展。作为我们主要发现的特例，我们获得了一些有趣的结果。