# Even and odd functions

## Even and odd functions

A function is said to be even if and only if .

A function is said to be odd if and only if .

The product of even functions is even, the product of odd functions is even, and the product of an even function and an odd function is odd. The sum of even functions is another even function and the sum of odd functions is an odd function. Functions that are neither even nor odd can be represented as the sum of an even and an odd function.

The integral of an even function on symmetric limits has the property

and is, in general nonzero, whereas the integral of an odd function on symmetric limits vanishes