Links

Tools

Export citation

Search in Google Scholar

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

Journal article published in 2011 by Zhi-Wei Sun
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Question mark in circle
Preprint: policy unknown
Question mark in circle
Postprint: policy unknown
Question mark in circle
Published version: policy unknown

Abstract

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 $π G$, one series involving both $π^3G$ and $π^2ζ(3)$, two series for $π K$, 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. ; Comment: 33 pages. Add the current (1.21), (1.54) and (1.55)