五参数超几何3F2(1)当一个或多个参数为整数或被整数隔开时：推导、回顾、奇特性及其他
Five Parameter Hypergeometric 3F2(1) when One or more Parameters are Integers or Separated by Integers: Derivations, Review, Exotics and More
AI总结：
本文探讨了超几何函数3F2(1)在参数为整数或被整数隔开时的推导、回顾及新结果，提供了一种简化求值的方法和通用恒等式。
摘要：
本文旨在全面探讨并仅探讨超几何3F2(1)。最初的目的是回顾文献中多年来推导出的许多恒等式，并展示它们可以通过仅使用少量初等恒等式以更简单的方式获得。这一目标已达成，耐心的读者会发现这一点。从另一个角度来看，本文是对过去半个世纪以来特定一组3F2(1)求值进展的综述，特别是那些至少有一个参数为整数或两个或更多参数被整数隔开的情况。结果是一组非常通用的恒等式（或技术），分析者在求值特定3F2(1)时可能会考虑作为起点。这是次要目标。然而，在此过程中，产生了调查他人提出的问题的诱惑。这导致了一些偏离，以及可能的新结果。读者被邀请跟随好奇心引导的路径，而非一条直接的综述路线。
英文摘要：
This work was intended to be all about, and only about, hypergeometric 3F2(1). The initial goal was to revisit many identities from the literature that have been derived over the years and show that they can be obtained in a simpler way armed, with only a minimum of elementary identities. That goal has been achieved as a (patient) reader will discover. In another sense, this work is a partial review of the last half-century's worth of progress in the evaluation of a particular set of 3F2(1), in particular those cases where at least one parameter is an integer or two or more parameters are separated by an integer. The result is a collection of very general identities (or techniques) that an analyst seeking to evaluate a particular 3F2(1), might want to consider as a starting point. That is the secondary goal. Along the way however, the temptation arose to investigate at least one of the unanswered questions that others have raised. This led to a few digressions, and some possibly new results. The reader is invited to follow where curiosity led me to depart from a straightforward review of the state-of-the-art.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
