Lotka's law,[1] named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law.
It describes the frequency of publication by authors in any given field.
be a constants depending on the specific field.
In Lotka's original publication, he claimed
Equivalently, Lotka's law can be stated as
Their equivalence can be proved by taking the derivative.
Assume that n=2 in a discipline, then as the number of articles published increases, authors producing that many publications become less frequent.
Lotka's law may be described using the Zeta distribution: for
It is the limiting case of Zipf's law where an individual's maximum number of publications is infinite.