For

$$\operatorname{For}\!\left(x, \ldots\right)$$

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).

$$\left\{f(a), f\!\left(a + 1\right), \ldots, f(b)\right\}$$

Typically, For(n, a, b) specifies iteration over $n$ from $a$ to $b$. The iteration is empty if $b < a$.

$$\sum_{n=a}^{b} f(n)$$

Typically, For(n, a, b) specifies iteration over $n$ from $a$ to $b$. The iteration is empty if $b < a$.

$$\int_{a}^{b} f(x) \, dx$$

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.

$$\lim_{x \to \pi} f(x)$$

In a limit or derivative operator, For(x, c) specifies the limit or differentiation point c.

Last updated: 2020-03-06 00:22:16