Chapter 11. Fourier Series

  1. André I. Khuri

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch11

Advanced Calculus with Applications in Statistics, Second Edition

Advanced Calculus with Applications in Statistics, Second Edition

How to Cite

Khuri, A. I. (2002) Fourier Series, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch11

Author Information

  1. University of Florida, Gainesville, Florida, USA

Publication History

  1. Published Online: 26 MAR 2003
  2. Published Print: 1 NOV 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A. C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J. B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F. M. Smith and
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884



  • characteristic function;
  • convergence;
  • convolution;
  • differentiation;
  • Fourier integral;
  • Fourier transform;
  • integration;
  • periodic function;
  • piecewise continuous;
  • Riemann integrable function;
  • time series;
  • trigonometric polynomial;
  • trigonometric series


This chapter provides a detailed study of Fourier series associated with Riemann-integrable functions. In particular, the chapter discusses conditions for the convergence of the series, and the conditions under which the series can be differentiated or integrated term by term. The Fourier integral and the Fourier transform are also included. The last section on applications in statistics includes applications in time series, Fourier series representation of distribution functions, regression modeling, and a study of characteristic functions.