For
Generator expression. This is a syntactical construct which does not represent a mathematical object on its own. The For expression defines the symbol passed as the first argument (here x) as a locally bound variable in the scope of the parent expression. Additional arguments ... specify an iteration range or evaluation point for x (the interpretation of these arguments depends on the parent operator).
Typically, For(n, a, b) specifies iteration over $n$ from $a$ to $b$. The iteration is empty if $b < a$.
Typically, For(n, a, b) specifies iteration over $n$ from $a$ to $b$. The iteration is empty if $b < a$.
In an integral operator, For(n, a, b) specifies a straight-line path for $x$ from $a$ to $b$. Swapping the endpoints negates the integral.
In a limit or derivative operator, For(x, c) specifies the limit or differentiation point c.