# accumulation

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4 matching pages ♦

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## 4 matching pages

##### 1: 1.9 Calculus of a Complex Variable

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►A point ${z}_{0}$ is a

*limit point*(*limiting point*or*accumulation point*) of a set of points $S$ in $\u2102$ (or $\u2102\cup \mathrm{\infty}$) 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: 18.39 Applications in the Physical Sciences

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►The Schrödinger operator essential singularity, seen in the accumulation of discrete eigenvalues for the attractive Coulomb problem, is mirrored in the accumulation of jumps in the discrete Pollaczek–Stieltjes measure as $x\to -1-$.
As the Coulomb–Pollaczek OP’s are members of the Nevai-Blumenthal class, this is, for $$, a physical example of the properties of the zeros of such OP’s, and their possible accumulation at $x=-1$, as discussed in §18.2(xi).
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##### 3: 3.8 Nonlinear Equations

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►However, to guard against the accumulation of rounding errors, a final iteration for each zero should also be performed on the original polynomial $p(z)$.
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##### 4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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►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). …