List of conjectural series for powers of ππ and other constants

preprint2014arXivOpen access

Abstract

The author gives the full list of his conjectures on series for powers of ππ 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−1π^{-1}, four series for π2π^2, two series for π−2π^{-2}, four series for π4π^4, two series for π5π^5, three series for π6π^6, seven series for ζ(3)ζ(3), one series for πζ(3)πζ(3), two series for π2ζ(3)π^2ζ(3), one series for ζ(3)2ζ(3)^2, three series involving both ζ(3)2ζ(3)^2 and π6π^6, one series for ζ(5)ζ(5), three series involving both ζ(5)ζ(5) and ζ(2)ζ(3)ζ(2)ζ(3), two series involving both πζ(5)πζ(5) and π3ζ(3)π^3ζ(3), three series involving ζ(7)ζ(7), three series for K=L(2,(⋅3))K=L(2,(\frac{\cdot}{3})), one series for the Catalan constant GG, two series for πGπG, one series involving both π3Gπ^3G and π2ζ(3)π^2ζ(3), two series for πKπK, two series involving L=L(4,(⋅3))L=L(4,(\frac{\cdot}3)), three series involving β(4)=L(4,(−4⋅))β(4)=L(4,(\frac{-4}{\cdot})), and four series for π2log⁡aπ^2\log a with a=2,3,(5+1)/2a=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.

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