What function was used for current record of decimal places of EM cnst

  • Context: Graduate 
  • Thread starter Thread starter mesa
  • Start date Start date
  • Tags Tags
    Current Em Function
Click For Summary

Discussion Overview

The discussion centers around the methods used to calculate the Euler-Mascheroni constant to an extremely high number of decimal places, specifically referencing the record set by Alexander J. Yee and Raymond Chan. Participants explore the functions and algorithms that may have been employed in achieving this record, as well as sharing links to relevant resources.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants note the record for the Euler-Mascheroni constant has reached over 119 billion decimal places, initially set at just over 29 billion.
  • One participant provides a link to MathWorld, suggesting that the fastest converging formula might be the one by Flajolet and Vardi from 1996, although they express uncertainty about the use of 'n' in that context.
  • Another participant mentions that Alexander J. Yee used the Brent-McMillan algorithm with Refinement for his calculations, referencing his website for further details.
  • Multiple participants share links to resources that detail the formulas and algorithms related to the Euler-Mascheroni constant.

Areas of Agreement / Disagreement

Participants generally agree on the record-setting achievements but express differing views on the specific methods and algorithms used, with no consensus on the best approach or function.

Contextual Notes

There is uncertainty regarding the details of the algorithms mentioned, particularly the application of 'n' in the Flajolet and Vardi formula, and the discussion does not resolve which method is definitively superior.

mesa
Gold Member
Messages
694
Reaction score
36
The record for the number of decimal places of accuracy for the Euler-Mascheroni constant stands at just over 29,000,000,000 decimal places set by Alexander J. Yee & Raymond Chan back in 2009. Does anyone know what function they used to set this record?

***EDIT***
On further searching the record now stands at 31,000,000,000 decimal places, Wow!
How do we update wikipedia? :P
***EDIT***
Make that 119,377,958,182 :biggrin:
 
Last edited:
Mathematics news on Phys.org
mesa said:
The record for the number of decimal places of accuracy for the Euler-Mascheroni constant stands at just over 29,000,000,000 decimal places set by Alexander J. Yee & Raymond Chan back in 2009. Does anyone know what function they used to set this record?

***EDIT***
On further searching the record now stands at 31,000,000,000 decimal places, Wow!
How do we update wikipedia? :P
***EDIT***
Make that 119,377,958,182 :biggrin:

Took care of it.
 
UltrafastPED said:
Formulas are listed here: http://mathworld.wolfram.com/Euler-MascheroniConstant.html

I looked through those before, it seems the fastest converging of the bunch is the one done by Flajolet and Vardi in '96 although I do not understand how the 'n' is used so could be wrong.

SteamKing said:
Took care of it.

And yet another reason why I love PF.
 
lurflurf said:
See Alexander J. Yee's site
http://www.numberworld.org/y-cruncher/algorithms.html
He used Brent-McMillan with Refinement.

I was on his site not too long ago, I have no idea how I miss these things...
Thanks for the link, it has exactly what I was asking for!