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Fourier Series pp 109-129 | Cite as

Some Special Series and Their Applications

  • R. E. Edwards
Part of the Graduate Texts in Mathematics book series (GTM, volume 64)

Abstract

In this chapter we assemble a few results about two special types of series, namely,
$$ \frac{1}{2} {{a}_{0}} + \sum\limits_{{n = 1}}^{\infty } {{{a}_{n}}\cos nx = \sum\limits_{{n \in z}} {{{c}_{n}}{{e}^{{inx}}},} } $$
where \({{c}_{n}} = \frac{1}{2} {{a}_{{\left| n \right|}}};\) and
$$\sum\limits_{n = 1}^\infty {{a_n}\sin nx = \sum\limits_{n \in z} {{c_n}{e^{inx}},} } $$
where cπ = (l/2i) sgn na|n|. We shall assume throughout that the an are real-valued, and write sN and σN for the Nth partial sum and the Nth Cesàro mean, respectively, of whichever series happens to be under discussion.

Keywords

Fourier Series Uniform Convergence Bounded Variation Pointwise Convergence Special Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1979

Authors and Affiliations

  • R. E. Edwards
    • 1
  1. 1.Institute for Advanced StudiesThe Australian National UniversityCanberraAustralia

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