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List of conjectural series for powers of $\pi$ and other constants

By Zhi-Wei Sun

Abstract

The author gives the full list of his conjectures on series for powers of $\pi$ 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 $\pi^{-1}$, four series for $\pi^2$, two series for $\pi^{-2}$, four series for $\pi^4$, two series for $\pi^5$, three series for $\pi^6$, seven series for $\zeta(3)$, one series for $\pi\zeta(3)$, two series for $\pi^2\zeta(3)$, one series for $\zeta(3)^2$, three series involving both $\zeta(3)^2$ and $\pi^6$, one series for $\zeta(5)$, three series involving both $\zeta(5)$ and $\zeta(2)\zeta(3)$, two series involving both $\pi\zeta(5)$ and $\pi^3\zeta(3)$, three series involving $\zeta(7)$, three series for $K=L(2,(\frac{\cdot}{3}))$, one series for the Catalan constant $G$, two series for $\pi G$, one series involving both $\pi^3G$ and $\pi^2\zeta(3)$, two series for $\pi K$, two series involving $L=L(4,(\frac{\cdot}3))$, three series involving $\beta(4)=L(4,(\frac{-4}{\cdot}))$, and four series for $\pi^2\log a$ 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.Comment: 33 pages. Add the current (1.21), (1.54) and (1.55

Topics: Mathematics - Classical Analysis and ODEs, Mathematics - Combinatorics, Mathematics - Number Theory, 33F05, 05A19, 11B65, 11M06
Year: 2014
OAI identifier: oai:arXiv.org:1102.5649
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