To 50 digits, here is the value of the Euler-Mascheroni constant
0.57721566490153286060651209008240243104215933593992
Computing it is just a loop. Compute the sum of 1/k.
tic
format long g
C = 0;
for k = 1:1e9
C = C + 1/k;
end
toc
C - log(k+0.5)
Elapsed time is 6.444622 seconds.
ans =
0.577215664902138
So, after 6.4 seconds and 1 billion terms, I was pretty close. You won't be able to get 50 decimal digits that way though. It as been a while, but in the documentation for eulerGamma in my HPF tool, I had these comments:
% Uses the Bessel function method from:
% http://numbers.computation.free.fr/Constants/Gamma/gamma.pdf
%
% See also:
% http://en.wikipedia.org/wiki/Euler?Mascheroni_constant
