关于Mező的一个问题及其向三类有理zeta级数的推广
On a problem of Mező and its generalizations to three classes of rational zeta series
AI总结：
本文以封闭形式求值了三类带附加参数的交错zeta级数，证明了涉及多重对数、不完全Gamma函数和指数积分的表达式，并重新发现了多位学者及Mező在《美国数学月刊》上提出的级数恒等式。
摘要：
我们以封闭形式求值了三类带有一个和两个附加参数的交错zeta级数。其中两类表示为多重对数的线性组合，而对于第三类，我们证明了包含不完全Gamma函数和指数积分的表达式。我们还提出了一些可从主要结果推导出的相关级数，以及一些以Fibonacci数和Lucas数为系数的级数。本文所提级数的特定情形将重新发现Zhang和Williams、Choi和Srivastava以及Orr等人建立的恒等式。我们还将重新发现Mező于2015年作为问题提案发表在《美国数学月刊》上的一个级数恒等式。
英文摘要：
We evaluate in closed form three special classes of alternating zeta series with one and two additional parameters. Two classes are expressed as linear combinations of polylogarithms while for the third class we prove an expression involving the incomplete gamma function and the exponential integral. We also present some related series that can be deduced from the main results as well as some series with Fibonacci and Lucas numbers as coefficients. Particular cases of the series presented here will be rediscoveries of identities established by Zhang and Williams, Choi and Srivastava, and Orr, among others. We will also rediscover a series identity published by Mező in 2015 as a problem proposal in the American Mathematical Monthly.
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