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I am very new to MATLAB and need to program this formula:
gamma = lim m -> inf [sum k=1 to m((1/k) - ln(m + .5)]
I'm not sure how to simultaneously compute a limit and a summation simultaneously.
I tried: euler = limit(sum((1/k)-ln(m+.5)), k = 1..m), m, inf)
but it isn't working.

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John D'Errico
John D'Errico 2016-2-9
编辑：John D'Errico 2016-2-9

1 个投票

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

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