A univariate function f(x) is said to be odd provided that f(-x) = - f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, x^3, the sine sin x, hyperbolic sine sinh x, tangent tan x, hyperbolic tangent tanh x, error function erf erf(x), inverse erf erf^(-1)(x), and the Fresnel integrals C(x), and S(x). An even function times an odd function is odd, and the product of two odd functions is even while the sum or difference of two nonzero functions is odd if and only if each summand function is odd. The product and quotient of two odd functions is an even function.
