Frequently Asked Questions
Does the harmonic series converge?
No. The infinite harmonic series one plus one half plus one third plus ... diverges to infinity, but very slowly. It exceeds 100 only around n equals 1.5 times 10 to the 43.
What is the Euler-Mascheroni constant?
The constant gamma about 0.5772 defined as the limit of H sub n minus the natural log of n as n goes to infinity. It appears throughout analytic number theory.
How accurate is the asymptotic formula?
Already excellent for moderate n. At n equals 10 the error is below 10 to the minus 4, and at n equals 1000 it is below 10 to the minus 12. For huge n the formula is far faster than summing directly.
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