accumulation point

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1: 1.9 Calculus of a Complex Variable

… ►A point $z_0$ is a limit point (limiting point or accumulation point) of a set of points $S$ in $ℂ$ (or $ℂ\cup \mathrm{\infty }$) if every neighborhood of $z_0$ contains a point of $S$ distinct from $z_0$. …Also, the union of $S$ and its limit points is the closure of $S$. …

2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►In unusual cases $N=\mathrm{\infty }$, even for all $\mathrm{\ell }$, such as in the case of the Schrödinger–Coulomb problem ($V=-r^{-1}$) discussed in §18.39 and §33.14, where the point spectrum actually accumulates at the onset of the continuum at $\lambda =0$, implying an essential singularity, as well as a branch point, in matrix elements of the resolvent, (1.18.66). …

3: 18.39 Applications in the Physical Sciences

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Figure 18.39.2: Coulomb–Pollaczek weight functions, $x\in [-1,1]$, (18.39.50) for $s=10$, $l=0$, and $Z=\pm 1$. …For $Z=-1$ the weight function, blue curve, is non-zero at $x=-1$, but this point is also an essential singularity as the discrete parts of the weight function of (18.39.51) accumulate as $k\to \mathrm{\infty }$, $x_k\to -1-$. Magnify

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