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Examples ofdivergent series
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There are usually five cribriform circular plates arranged in two longitudinal and slightlydivergentseries.
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Understanding the meaning of algebraically generateddivergentseriesremained a frustration, but one he was willing to leave to future generations.
From theCambridge English Corpus
Taking regularity, linearity and stability as axioms, it is possible to sum manydivergentseriesby elementary algebraic manipulations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.He also made major investigations in the areas of gamma functions, modular forms,divergentseries, hypergeometric series and prime number theory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Summation ofdivergentseriesis also related to extrapolation methods and sequence transformations as numerical techniques.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Many summation methods are used in mathematics to assign numerical values even to adivergentseries.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Generally speaking, it is dangerous to manipulate infinite series as if they were finite sums, and it is especially dangerous fordivergentseries.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is adivergentseries, meaning that it lacks a sum in the usual sense.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The harmonic series is a classic example of adivergentserieswhose terms limit to zero.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Divergentseriesare on the whole devil's work, and it is a shame that one dares to found any proof on them.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Zeta function regularization is used as one possible means of regularization ofdivergentseriesand divergent integrals in quantum field theory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Since then, mathematicians have explored many different summability methods fordivergentseries.
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This example is from Wikipedia and may be reused under a CC BY-SA license.However, such theoretically efficient methods usedivergent-seriesstepsize rules, which were first developed for classical subgradient methods.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Since justifications were given that useddivergentseries, these methods had a bad reputation from the point of view of pure mathematics.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Classical subgradient methods usingdivergent-seriesrules are much slower than modern methods of convex minimization, such as subgradient projection methods, bundle methods of descent, and nonsmooth filter methods.
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This example is from Wikipedia and may be reused under a CC BY-SA license.A generalized definition of the sum of adivergentseriesis called a summation method or summability method, which sums some subset of all possible series.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Strictly speaking these are not really summation methods fordivergentseries, as by definition a series is divergent only if these methods do not work, but are included for completeness.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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