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
Famous quotes containing the words harmonic and/or number:
“For decades child development experts have erroneously directed parents to sing with one voice, a unison chorus of values, politics, disciplinary and loving styles. But duets have greater harmonic possibilities and are more interesting to listen to, so long as cacophony or dissonance remains at acceptable levels.”
—Kyle D. Pruett (20th century)
“Without claiming superiority of intellectual over visual understanding, one is nevertheless bound to admit that the cinema allows a number of æsthetic-intellectual means of perception to remain unexercised which cannot but lead to a weakening of judgment.”
—Johan Huizinga (1872–1945)