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Johndcook

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Computing the Euler-Mascheroni Constant

  • The Euler-Mascheroni constant can be computed by evaluating an equation with a large n, but convergence is slow and rounding errors accumulate.
  • A more efficient approach involves adding an extra factor of ½ in the log term, which converges faster to the Euler-Mascheroni constant.
  • Comparing the two methods, the error in the first method with n = 4000 is similar to the error in the second method with n = 16.
  • Software like y-cruncher has been used to set world records for computing constants like π and the Euler-Mascheroni Constant, which is particularly challenging to compute.

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