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Fractional (L\'{e}vy-type) operators are known to be spatially nonlocal. Thisbecomes an issue if confronted with a priori imposed exterior Dirichletboundary data. We address spectral properties of the prototype example of theCauchy operator $(-\Delta )^{1/2}$ in the interval $D=(-1,1) \subset R$, with afocus on functional shapes of lowest eigenfunctions and their fall-off at theboundaries of $D$. New high accuracy formulas are deduced for approximateeigenfunctions. We analyze how their shape reproduction fidelity is correlatedwith the evaluation finesse of the corresponding eigenvalues.

Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well