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A \emph{functional equation} is an equation whose unknowns are functions.
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A functional equation is an equation whose unknowns are functions.
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| $f(x+y) = f(x) + f(y),\quad f(x\cdot y) = f(x) \cdot f(y)$ are examples of such |
$f(x+y) = f(x) + f(y),\quad f(x\cdot y) = f(x) \cdot f(y)$ are examples of such |
| equations. The systematic study of these didn't begin before the 1960's, |
equations. The systematic study of these didn't begin before the 1960's, |
| although various mathematicians have been studying them before, including |
although various mathematicians have been studying them before, including |
| Euler and Cauchy just to mention a few. |
Euler and Cauchy just to mention a few. |
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| Functional equations appear many \PMlinkescapetext{places}, for example, |
Functional equations appear many \PMlinkescapetext{places}, for example, |
| the gamma function and Riemann's zeta function both satisfy functional equations. |
the gamma function and Riemann's zeta function both satisfy functional equations. |
