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

Sine Kano 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1979

Authors and Affiliations

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

Personalised recommendations