arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1102.5649math.CAmath.COmath.NT
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$π$和其他常数的幂级数列表

List of conjectural series for powers of $π$ and other constants

Zhi-Wei Sun

摘要:

作者给出了完整的列表,他的系列的权力$π$和其他重要常数分散在他的一些公共文件或他的私人日记。该列表包含234个合理的地理序列。清单上有178个合理的$π^{-1}$系列,4个$π^2$系列,2个$π^{-2}$系列,4个$π^4$系列,2个$π^5$系列,3个$π^6$系列,7个$ζ(3)$系列,1个$πζ(3)$系列,2个$π^2ζ(3)$系列,1个$ζ(3)^2$系列,3个$ζ(3)^2$和$π^6$同时涉及的系列,1个$ζ(5)$系列,涉及$ζ(5)$和$ζ(2)ζ(3)$两者的三个系列,涉及$πζ(5)$和$π^3ζ(3)$两者的两个系列,涉及$ζ(7)$的三个系列,用于$K=L(2,(\frac{\cdot}{3}))$的三个系列,用于加泰罗尼亚常数$G$的一个系列,用于$πG$的两个系列,涉及$π^3G$和$π^2ζ(3)$两者的一个系列,用于$πK$的两个系列,涉及$L=L(4,(\frac{\cdot}3))$的两个系列,涉及$β(4)=L(4,(\frac{-4}{\cdot}))$的三个系列,$π^2\log a$和$a=2,3,(\sqrt5+1)/2$的四个系列。当且仅当有完整的身份证明时,一个序列的代码才加下划线。

英文摘要:

The author gives the full list of his conjectures on series for powers of $π$ and other important constants scattered in some of his public papers or his private diaries. The list contains 234 reasonable conjectural series. On the list there are 178 reasonable series for $π^{-1}$, four series for $π^2$, two series for $π^{-2}$, four series for $π^4$, two series for $π^5$, three series for $π^6$, seven series for $ζ(3)$, one series for $πζ(3)$, two series for $π^2ζ(3)$, one series for $ζ(3)^2$, three series involving both $ζ(3)^2$ and $π^6$, one series for $ζ(5)$, three series involving both $ζ(5)$ and $ζ(2)ζ(3)$, two series involving both $πζ(5)$ and $π^3ζ(3)$, three series involving $ζ(7)$, three series for $K=L(2,(\frac{\cdot}{3}))$, one series for the Catalan constant $G$, two series for $πG$, one series involving both $π^3G$ and $π^2ζ(3)$, two series for $πK$, two series involving $L=L(4,(\frac{\cdot}3))$, three series involving $β(4)=L(4,(\frac{-4}{\cdot}))$, and four series for $π^2\log a$ with $a=2,3,(\sqrt5+1)/2$. The code of a conjectural series is underlined if and only if a complete proof of the identity is available.

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。

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