functional equation FunctionalEquation 2002-10-24 22:12:54 2006-09-26 16:48:51 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions \usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here A \emph{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 \PMlinkescapetext{places}, for example, the gamma function and Riemann's zeta function both satisfy functional equations.