The question title pretty much says it all.
In derivations where there's some fancy footwork being done with indices, I find expressions like
∑i≠kxi
a bit too vague. On the other hand, this is explicit enough, but just too unwieldy and awkward-looking:
∑i∈{0,1,…,k−1,k+1,…,n−1,n}xi
(Of course, I can invent my own notation, but I consider this the "the nuclear option.")
Answer
I've seen {0,…,ˆk,…,n}, but that's not much shorter.
Alternatively, [n] is often shorthand for {1,…,n}, so you could use [n]∖{k}.
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