# What is considered to be a Heap’s law?

I’m not sure if this is more physics question than mathematics but anyways. Something is usually said to follow Heap’s law if it is given as a function $$V(n)=K n^b$$, where $$b$$ and $$K$$ are constants (source). Given this ’definition’ it should be okey to say that a function like $$\sqrt{t}$$ is one possibility. However, if we have something like $$\sqrt{1+t}$$ or $$\sqrt{t}+1$$, are these still considered to have the correct form to be Heap’s?

I would assume yes? I guess this same question applies to power laws..

• I don´t think so since both are not $\textrm{homogeneous}$ functions. – callculus Jun 12 at 20:58