## Euler-Mascheroni Constant good to about 316 decimals… (cf. Knuth 1962)

57721 56649 01532 86060 65120 90082 40243 10421 59335 93992

35988 05767 23488 48677 26777 66467 09369 47063 29174 67495

14631 44724 98070 82480 96050 40144 86542 83622 41739 97644

92353 62535 00333 74293 73377 37673 94279 25952 58247 09491

60087 35203 94816 56708 53233 15177 66115 28621 19950 15079

84793 74508 57057 40029 92135 47861 46694 02960 43254 21519

05877 55352 67331 39858

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Glaisher in 1999 calculated Gamma to 108000000 decimal places

LudovicusSeptember 26, 2014 at 6:33 pm

As I recall, the Gamma function has the property that Gamma’ (1) = -gamma, and Gamma'(2) = 1-gamma.

Those are identities that I find interesting. As a test of PARI/gp and for entertainment, I computed numerically (estimated) Gamma'(2), obtaining say dy/dx . From that, I got the estimate:

gamma = 1-Gamma'(2) ~= 1 – dy/dx . Another thing I did was to compare with Knuth’s original article in Math. Comput. I believe his estimate in a Table was to 1200 to 1300 decimals places.

meditationataeSeptember 27, 2014 at 12:16 am

It seems to me the computation of the Euler-Mascheroni constant to 108 million decimals was done by X. Gourdon and P. Demichel .

meditationataeSeptember 27, 2014 at 12:32 am