How to write mathematically the triple operation and so on?

Question

We know that unary and binary opertions could be represened by symbolically $\: \circ x, \: y \circ z \quad$ respectively. How about the ones involve three and more.

Answer 1

After you have three elements or more to compose, it will become a little awkward to use a single mark between them to denote composition. It would be quite silly to, for example, arrange the inputs equidistantly around a single symbol.

At that rate, any operation can be written with functional notation much more easily: given the operation $F: X^n\to X$ you write $F(x_1,\ldots, x_n)$ for the "product of $n$ elements."

Answer 2

There's no reason to use an operator notation that implicitly has only a left side and a right side. Why not something like $\stackrel{y\;\;z}{x}$ instead?

Some actuarial notation has symbol decorations at every point of the compass. See this Wikipedia page, for example.