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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(...

This is mostly a reference request. I'm working with complex coefficients, although all I have in mind have integer coefficients. Let $a=(a(n))_{n\ge 1}$ be a sequence, say of integers (I have non-...

Let $x$ be a variable. Define the following family of sequences (reminiscent of Lucas polynomials) according to the rule: $P_0(x):=0, P_1(x):=1$ and for $n\geq2$ by $$P_n(x)=xP_{n-1}(x)-P_{n-2}(x).$$ ...