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)


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.


Sine Kano 


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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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