Riemann Zeta函数、Dirichelet Eta函数的积分和级数表示及相关结果
Integral and Series Representations of Riemann's Zeta function, Dirichelet's Eta Function and a Medley of Related Results
摘要：
给出并研究了Riemann Zeta函数和Dirichelet Eta（交替Zeta）函数的围道整表示。这些表示自然地从1800年开发的方法中流出，但不知何故，它们没有出现在标准的参考摘要，教科书或文献中。使用这些表示作为基础，交替推导已知系列和整表示的Zeta和Eta函数得到一个统一的基础上，不同的教科书的方法，结果开发，似乎是新的。
英文摘要：
Contour integral representations for Riemann's Zeta function and Dirichelet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800's, but somehow they do not appear in the standard reference summaries, textbooks or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the Zeta and Eta function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.
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。
