How to find Euler's Constant
17 views (last 30 days)
Show older comments
christina andrews
on 9 Feb 2016
Edited: John D'Errico
on 9 Feb 2016
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.
0 Comments
Accepted Answer
John D'Errico
on 9 Feb 2016
Edited: John D'Errico
on 9 Feb 2016
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
0 Comments
More Answers (0)
See Also
Categories
Find more on Dates and Time in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!