In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers:
This also equals n times the inverse of the harmonic mean of these natural numbers.
Harmonic numbers were studied in antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function, and appear in various expressions for various special functions.
When the value of a large quantity of items has a Zipf's law distribution, the total value of the n most-valuable items is the n-th harmonic number. This leads to a variety of surprising conclusions in the Long Tail and the theory of network value.
Read more about Harmonic Number: Calculation, Special Values For Fractional Arguments, Generating Functions, Applications
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