divergent
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1: 25.17 Physical Applications
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►Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect).
It has been found possible to perform such regularizations by equating the divergent sums to zeta functions and associated functions (Elizalde (1995)).
2: 36.14 Other Physical Applications
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►These are the structurally stable focal singularities (envelopes) of families of rays, on which the intensities of the geometrical (ray) theory diverge.
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3: 1.6 Vectors and Vector-Valued Functions
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►The divergence of a differentiable vector-valued function is
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1.6.21
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1.6.27
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Gauss’s (or Divergence) Theorem
…4: 8.25 Methods of Computation
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►For large the corresponding asymptotic expansions (generally divergent) are used instead.
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5: 9.17 Methods of Computation
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►Since these expansions diverge, the accuracy they yield is limited by the magnitude of .
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6: 22.19 Physical Applications
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►As from below the period diverges since are points of unstable equilibrium.
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►As from below the period diverges since is a point of unstable equlilibrium.
…As from above the period again diverges.
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7: 2.6 Distributional Methods
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§2.6(i) Divergent Integrals
… ►Although divergent, these integrals may be interpreted in a generalized sense. … ►The fact that expansion (2.6.6) misses all the terms in the second series in (2.6.7) raises the question: what went wrong with our process of reaching (2.6.6)? In the following subsections, we use some elementary facts of distribution theory (§1.16) to study the proper use of divergent integrals. … ►On inserting this identity into (2.6.54), we immediately encounter divergent integrals of the form …However, in the theory of generalized functions (distributions), there is a method, known as “regularization”, by which these integrals can be interpreted in a meaningful manner. …8: Bibliography W
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Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series.
Computer Physics Reports 10 (5-6), pp. 189–371.
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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations.
Computers in Physics 10 (5), pp. 496–503.
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9: 16.2 Definition and Analytic Properties
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►On the circle the series (16.2.1) is absolutely convergent if , convergent except at if , and divergent if , where
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►In general the series (16.2.1) diverges for all nonzero values of .
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10: 1.9 Calculus of a Complex Variable
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