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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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Two-variable continuous function which results in an integer if and only if arguments are in...

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties: $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$. $f(m,n) \le f(r,s)$ …
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