Name for a function that can handle arbitrary number of arguments I am writing a proof, which uses functions that can handle an arbitrary number of parameters like summing, or averaging. In other words, I'm referring to functions like:

$f(x_1, ... x_n) = \sum_i x_i$, or 

$f(x_1, ... x_n) = 1/n \sum_i x_i$, or even

$f(x_1, ... x_n) = \sum_i i \cdot x_i$

Clearly, $n$ can be arbitrary and these definitions would still make sense. I'd like to call these functions a name. Is there an existing name for such functions?

As an example, I'd like to be able to say: "Let $f$ be a ______ function that acts on some (or all) of the elements of $S$" (So here $f$ would be any function that accepts any number of elements from $S$ as arguments". What's the right way to word this?
As hinted by Fabio Somenzi and JonathanZ, in the context of computer science you can call these kind of functions variadic or aggregating. 

By the way, you can easily define this kind of function in a mathematically rigorous way. The intuition is that a function $f$ would have an arbitrary arity, i.e. $f$ would accept any number of elements from a set $S$ as arguments. From a rigorous prospective, you can say the domain of $f$ is the set $S^*$ (denoted also by $S^{&lt;\omega}$) of finite sequences of elements of $S$, i.e.

\begin{align}
S^* = \bigcup_{n \in \mathbb{N}} \overbrace{S \times \dots \times S}^{n \text{ times } S}.
\end{align}

So, for all $n \in \mathbb{N}$, $s_1, \dots, s_n \in S$ iff $(s_1, \dots, s_n) \in S^*$: in other words, $S^*$ contains all and only the tuples of elements of $S$, for every (finite) length. 

Strictly speaking, the function $f$ defined in this way is unary (with respect to the domain $S^*$), but it perfectly translates the idea that $f$ has an arbitrary arity (with respect to $S$). How powerful the language of mathematics is!
The term for the number of arguments a function takes is arity and for arbitrary (but finite) arguments is the somewhat unimaginative n-ary.