Functional equation

In mathematics, a functional equation is a relationship between the values of a function at different arguments.

Examples

 * Any periodic function has a functional equation of the form $$f(x+p) = f(x)$$ where p is the period.
 * Examples of periodic functions include trigonometric functions and elliptic functions.
 * The gamma function has a functional equation relating $$\Gamma(z)$$ to $$\Gamma(z-1)$$.
 * The Riemann zeta function has a function equation relating the value of $$\zeta(s)$$ to $$\zeta(1-s)$$.