An odd function is a function for which . Examples of odd functions include , , the sine , hyperbolic sine , tangent , hyperbolic tangent , error function erf , inverse erf , and the Fresnel integrals , and .

An even function times an odd function is odd, and the product of two odd functions is even.

If an even function is differentiable, then its derivative is an odd function. Similarly, if an odd function is differentiable, then its derivative is an even function.

Since an odd function is zero at the origin, it follows that the Maclaurin series of an odd function contains only odd powers.

CITE THIS AS:

Weisstein, Eric W. "Odd Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/OddFunction.html