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.
- 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
- Cheng, Sui Sun; Wendrong Li (2008). Analytic solutions of Functional equations. 5 Toh Tuck Link, Singapore 596224: World Scientific Publishing Co.. ISBN 13 978-981-279-334-8.