In the paper Continued-Fraction Expansions for the Riemann Zeta Function and Polylogarithms by Djurdje Cvijovic and Jacek Klinowski, there is a claim that I cannot reproduce. In the abstract they claim "For example, the 11th approximants for all ζ(n), n ≥ 2, give values with an error of less than 10^(−9)." When I implement the algorithms they describe, however, the 11th approximant for ζ(2) is 1.62328... which has an error of more than 0.02. I have carefully checked that my implementation is correct. I was wondering if anyone has been able to verify this problem?

  • $\begingroup$ The least they could have done was to give an explicit example, say for $\zeta(5)$, so one can check if there was a typo in their algorithms. $\endgroup$ – Tito Piezas III Aug 16 '15 at 5:51

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