# Functional equation  Main Article Talk Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] This editable Main Article is under development and not meant to be cited; by editing it you can help to improve it towards a future approved, citable version. These unapproved articles are subject to a disclaimer. [edit intro]

In mathematics, a functional equation is an implicit way to specify some mathematical function . Often, the functional equation relatte values of a function at different arguments. Usually, the solution of a functional equation is supposed to be a holomorphic function, although some functional equations were initially established for functions of a discrete variable; see for example the Ackermann functions.

## Examples

• Any periodic function has a functional equation of the form where p is the period.
• The gamma function has a functional equation relating to .
• The Riemann zeta function has a function equation relating the value of to .
• Superfunction of a given function is solution of functional equation .
• Abel equation
• Schroeder equation