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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Can we find a closed form formula for this function?

I'm interested in this function $$ h(m,n) = \operatorname{sgn}\Bigl(\lim_{w \to \infty}{\sum_{x_1=1}^{w}\dotsi\sum_{x_u=1}^{w}\dfrac{1}{1 + wp^2(m,n,x_1,\dotsc,x_u)}}\Bigr) $$ where $p$ is a polynomia …