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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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Are there such numbers?

Maybe better to ask for help on this question here: Are there eight numbers $0< x_{1},\ldots,x_{4},y_{1},\ldots,y_{4}<1$, such that $$ \frac{\max\left(\left(x_{i}-x_{j}\right){}^{2}+\left(y_{i}-y_{j}\ …