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List of conjectural series for powers of π and other constants

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arxiv 1102.5649 v47 pith:QF74WO7Z submitted 2011-02-28 math.CA math.COmath.NT

List of conjectural series for powers of π and other constants

classification math.CA math.COmath.NT
keywords serieszetainvolvingthreelistcdotconjecturalfour
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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  1. Series for $1/\pi$ arising from Cauchy product

    math.NT 2026-04 unverdicted novelty 5.0

    Proves a conjectured series for 1/π and derives two analogous cubic-polynomial series using Cauchy products and hypergeometric transformations.