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..

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

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