Chapter 2. Series Expansions of Arbitrary Functions

  1. R. Courant,
  2. D. Hilbert

Published Online: 24 DEC 2007

DOI: 10.1002/9783527617210.ch2

Book Title

Methods of Mathematical Physics, Volume I

Methods of Mathematical Physics, Volume I

Additional Information

How to Cite

Courant, R. and Hilbert, D. (2007) Series Expansions of Arbitrary Functions, in Methods of Mathematical Physics, Volume I, Wiley-VCH Verlag GmbH, Weinheim, Germany. doi: 10.1002/9783527617210.ch2

Publication History

  1. Published Online: 24 DEC 2007
  2. Published Print: 19 APR 1989

ISBN Information

Print ISBN: 9780471504474

Online ISBN: 9783527617210

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CHAPTER TOOLS

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Keywords:

  • fundamental;
  • vectors;
  • homogeneous;
  • orthogonalization;
  • approximation;
  • mathematical

Summary

This chapter contains sections titled:

  • Orthogonal systems of functions

  • The accumulation principle for functions

  • Measure of independence and dimension number

  • Weierstrass's approximation theorem. Completeness of powers and of trigonometric functions

  • Fourier series

  • The Fourier integral

  • Examples of Fourier integrals

  • Legendre polynomials

  • Examples of other orthogonal systems

  • Supplement and problems

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