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Parametric Continued Fractions for $\pi^2$, $\zeta(3)$, and other Constants

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arxiv 2304.11727 v1 pith:OLRSJXY2 submitted 2023-04-23 math.NT math.CO

Henri Cohen This is my paper · ORCID
classification math.NTmath.CO
keywords constantscontinuedfractionsotherzetadegreesextensivefamilies
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abstract

We give an extensive list of parametrized families of polynomial continued fractions of smallest possible degrees for $\pi^2$ and $\zeta(3)$, and mention similar results for other constants.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fast Ramanujan-type Series for Logarithms. Part I

    math.NT 2025-06 conditional novelty 7.0 of 10

    The paper introduces new, mostly proven hypergeometric series for log 2, log 3, and log 5 with lower binary splitting costs than Machin-type formulas, plus a variable-p family.

  2. Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary

    math.NT 2026-07 conditional novelty 6.5 of 10

    A theory-plus-dictionary of polynomial-type continued fractions with explicit convergence rates and Apéry-style accelerations, mostly new or newly quantified.

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