2011/02/28 by Zhi‐Wei Sun, Sun, Zhi-Wei · 2 citations
Mathematics · #05A19 #11B65 #11M06 #33F05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1102.5649
openalex publication_date 2011/02/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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 π2, two series for π-2, four series for π4, two series for π5, three series for π6, seven series for ζ(3), one series for πζ(3), two series for π2ζ(3), one series for ζ(3)2, three series involving both ζ(3)2 and π6, one series for ζ(5), three series involving both ζ(5) and ζ(2)ζ(3), two series involving both πζ(5) and π3ζ(3), three series involving ζ(7), three series for K=L(2,((⋅)/(3))), one series for the Catalan constant G, two series for πG, one series involving both π3G and π2ζ(3), two series for πK, two series involving L=L(4,(\frac⋅3)), three series involving β(4)=L(4,((-4)/(⋅))), and four series for π2log a with a=2,3,(√5+1)/2. The code of a conjectural series is underlined if and only if a complete proof of the identity is available.