Notation for a function from all members of a tuple minus one.

Is there any compact, mainstream notation for a function from all members of a tuple minus one? What I have in mind is

$f\left(a_{1},\ldots,a_{n}\right)$ (except for $a_{i}$) $=a_{i}$

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Is it a set, or a tuple? –  Arturo Magidin Jul 11 '12 at 20:39
A tuple, of course. Editing. Thanks. –  Schiphol Jul 11 '12 at 20:40
I have seen $f(a_1,\dots,\hat a_i,\dots,a_n)$, though of course it must be explained when it’s introduced. –  Brian M. Scott Jul 11 '12 at 20:40
If you mean an ordered tuple, then a common notation for $$(a_1,a_2,\ldots,a_{i-1},a_{i+1},\ldots,a_n)$$ is $$(a_1,a_2,\ldots,\widehat{a_i},\ldots,a_n).$$ But it is usually specified in text what it means the first time it is used.
I usually see this denoted $f(a_1,\ldots,\hat a_i,\ldots,a_n)$, with the $\hat\cdot$ sumbol used to denote exclusion.