A Simple Derivation of the Heap's Law from the Generalized Zipf's Law

TL;DR

This paper provides a straightforward derivation of Heaps' law from the generalized Zipf's law, clarifying the relationship between vocabulary growth and word frequency distribution.

Contribution

It offers a simple formal derivation linking Heaps' law to the generalized Zipf's law, enhancing theoretical understanding.

Findings

Heaps' law can be derived from the generalized Zipf's law.

The derivation clarifies the mathematical relationship between vocabulary size and word frequency.

The approach simplifies understanding of language growth dynamics.

Abstract

I reproduce a rather simple formal derivation of the Heaps' law from the generalized Zipf's law, which I previously published in Russian.