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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma(z)} to $\Gamma (z-1)$.
• The Riemann zeta function has a function equation relating the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \zeta(s)} to $\zeta (1-s)$.