accumulation
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4 matching pages
1: 1.9 Calculus of a Complex Variable
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►A point is a limit point (limiting point or accumulation point) of a set of points in (or ) if every neighborhood of contains a point of distinct from .
…Also, the union of and its limit points is the closure of .
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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 .
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 , 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 .
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4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►In unusual cases , even for all , such as in the case of the Schrödinger–Coulomb problem () discussed in §18.39 and §33.14, where the point spectrum actually accumulates at the onset of the continuum at , implying an essential singularity, as well as a branch point, in matrix elements of the resolvent, (1.18.66).
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