# Functional equation

From Citizendium, the Citizens' Compendium

In mathematics, a **functional equation** is an implicit way to specify some mathematical function
^{[1]}.
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.- Examples of periodic functions include trigonometric functions and elliptic functions.

- 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

## See also

## References

- ↑
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.