# functional equation

A functional equation is an equation whose unknowns are functions.

$f(x+y)=f(x)+f(y),\quad f(x\cdot y)=f(x)\cdot f(y)$ are examples of such equations. The systematic study of these didn’t begin before the 1960’s, although various mathematicians have been studying them before, including Euler 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.

Title functional equation FunctionalEquation 2013-03-22 13:06:53 2013-03-22 13:06:53 jgade (861) jgade (861) 9 jgade (861) Definition msc 39B05 Equation