Difference and Functional Equations
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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for functions satisfying f(x*y)=f(x)+f(y) and enquire whether the logarithm function f(x)=log(x) is the only solution. (It's not.) In some cases the nature of the answer is different when we insist that the functional equation hold for all real x, or all complex x, or only those in certain domains, for example. A special case involves difference equations, that is, equations comparing f(x) - f(x-1), for example, with some expression involving x and f(x). In some ways these are discrete analogues of differential equations; thus we face similar questions of existence and uniqueness of solutions, global behaviour, and computational stability. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
|Math Topics:||Difference Equations|
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