divergence theorem
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6 matching pages
1: 1.6 Vectors and Vector-Valued Functions
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Gauss’s (or Divergence) Theorem
…2: 15.2 Definitions and Analytical Properties
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(c)
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Diverges when .
3: 2.1 Definitions and Elementary Properties
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►For example, if is analytic for all sufficiently large in a sector and as in , being real, then as in any closed sector properly interior to and with the same vertex (Ritt’s theorem).
This result also holds with both ’s replaced by ’s.
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►Let be a formal power series (convergent or divergent) and for each positive integer ,
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4: 1.9 Calculus of a Complex Variable
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DeMoivre’s Theorem
… ►Cauchy’s Theorem
… ►Liouville’s Theorem
… ►If the limit exists, then the double series is convergent; otherwise it is divergent. … ►Dominated Convergence Theorem
…5: 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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6: 2.7 Differential Equations
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►Hence unless the series (2.7.8) terminate (in which case the corresponding is zero) they diverge.
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►For irregular singularities of nonclassifiable rank, a powerful tool for finding the asymptotic behavior of solutions, complete with error bounds, is as follows:
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