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I was reading the book (Almost) Impossible Integrals, Sums and Series. The author used a method involving taking partial derivatives of the Beta Function to solve some integrals. $$B(x,y)=\int_0^1u^{x-...

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(...