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)
“In many ways, life becomes simpler [for young adults]. . . . We are expected to solve only a finite number of problems within a limited range of possible solutions. . . . It’s a mental vacation compared with figuring out who we are, what we believe, what we’re going to do with our talents, how we’re going to solve the social problems of the globe . . .and what the perfect way to raise our children will be.”
—Roger Gould (20th century)