Evaluation of ζ(2) by the definition (sort of) [HP42S & HP71B]

11012021, 05:04 AM
Post: #15




RE: Evaluation of ζ(2) by the definition (sort of) [HP42S & HP71B]
(11012021 12:56 AM)Albert Chan Wrote: We can get the CF correction formula, using Euler–Maclaurin formula (see #9) Thank you very much! I am not an expert and cannot fully grasp what you have done, but it looks like you have a proof. Almost three hundred years ago, before tackling the Basel problem, Euler evaluated the series to a few decimal digits using the EulerMacLaurin method, incidentally the same method used in these RPL programs. The continued fraction correction appears to require less computational effort to obtain the same number of digits. 

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