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Yet another π formula
01-08-2021, 01:24 AM
Post: #13
RE: Yet another π formula
(01-07-2021 09:56 PM)Albert Chan Wrote:  
(01-07-2021 12:57 PM)Gerson W. Barbosa Wrote:  Great! The continued fraction part is left unproved, however. But that would not be easy, I presume.

"Wasicki's formula" had first term converge to pi, correction converge to 0. QED

Were the correction term simply 1/(2n*(n + 1)) then this proof would still hold. Perhaps I should say “prove that the continuous fraction is equivalent to the optimal correction polynomial expression to the series”. That would be really hard, at least for me. If you find a valid proof then the formula should be renamed as “Wasicki-Chan Formula” or more appropriately “Chan-Wasicki Formula”. Anyone can easily find such formulae. Anyone or anything – even Mathematica and W/A can, I think. But only a few can prove them. Anyway nowadays these formulae are just useless mathematical curiosities.

(01-07-2021 09:56 PM)Albert Chan Wrote:  As to the gain of 25/12 digits per term, it tested OK even with 10,000 digits precision. Smile

Thank you for performing these tests. Much appreciated!
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Messages In This Thread
Yet another π formula - Gerson W. Barbosa - 01-04-2021, 08:41 PM
RE: Yet another π formula - Albert Chan - 01-05-2021, 10:50 PM
RE: Yet another π formula - Albert Chan - 01-06-2021, 01:32 AM
RE: Yet another π formula - Albert Chan - 01-07-2021, 09:56 PM
RE: Yet another π formula - Gerson W. Barbosa - 01-08-2021 01:24 AM
RE: Yet another π formula - toml_12953 - 01-06-2021, 02:10 AM
RE: Yet another π formula - ttw - 01-06-2021, 03:44 AM
RE: Yet another π formula - Albert Chan - 01-09-2021, 09:22 PM
RE: Yet another π formula - Albert Chan - 11-06-2021, 06:28 PM



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