Lotka's law

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.