Question about notation to depict multiplication $\cdot$ or $\star$ or nothing at all?

Question

I see different documents using $\cdot$ or $\star$ to depict multiplication.

For e.g. some use $4.5.6 = 120$ while others may be use $4\star 5\star 6 = 120$.

And in case it involves brackets, I also see stuff like

$e(x) = f(x)g(x)h(x)$

or

$e(x) = f(x)\cdot g(x) \cdot h(x)$

or

$e(x) = f(x)\star g(x) \star h(x)$

Are there any rules?

Answer 1

There are (as is the case with so many notation-related questions) no hard rules, though, as Bruno B. pointed out it's always good practice to not re-use symbols. Personally I think most mathematicians will prefer $\cdot$ (\cdot in LaTeX), and in the case of the function applications I think leaving the symbol completely is fine too.