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 $\zeta (1-s)$.