functional equation

A functional equation is an equation whose unknowns are functions.

$f(x+y)=f(x)+f(y),f(x\cdot y)=f(x)\cdot f(y)$ are examples of suchequations. The systematic study of these didn’t begin before the 1960’s,although various mathematicians have been studying them before, includingEuler and Cauchy just to mention a few.

Functional equations appear many , for example,the gamma function and Riemann’s zeta function both satisfy functional equations.