How to denote a function of all but one parameter (notation question)

Question

Say I have $n$ variables, $x_1,\dots,x_n$ and $n$ functions $f_i$ such that $f_i$ is a function of $x_1,\dots,x_{i-1},x_{i+1},\dots,x_n$, but not $x_i$.

Is there a more compact way of denoting this than

$$f_i(x_1,\dots,x_{i-1},x_{i+1},\dots,x_n) = \dots?$$

I apologize for the trivial question, but I had no idea what to search or even how to phrase this succinctly.

Answer 1

Sometimes people use $\hat{x}_j$ to denote the vector of $x$ with $x_j$ missing.