An equation of the form f(x, y, ...) = 0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many properties of functions can be determined by studying the types of functional equations they satisfy. For example, the gamma function Γ(z) satisfies the functional equations Γ(1 + z) | = | z Γ(z) Γ(1 - z) | = | -z Γ(-z).

Abel's duplication formula | Abel's functional equation | functional analysis | reflection relation