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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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Straight line on the Poincare disk hitting points almost everywhere

Consider the tiling of the Poincare disk $\mathbb{D}$ by identified octagons (i.e., representing a torus with genus 2). Suppose inside each octagon is a subset A such that the octagon minus A is a se …
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