Functional equation

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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.
  • 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

  1. 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.