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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. I. Functions whose early derivatives are continuous
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by J. N. Lyness PDF
Math. Comp. 24 (1970), 101-135 Request permission

Abstract:

The Möbius inversion technique is applied to the Poisson summation formula. This results in expressions for the remainder term in the Fourier coefficient asymptotic expansion as an infinite series. Each element of this series is a remainder term in the corresponding Euler-Maclaurin summation formula, and the series has specified convergence properties. These expressions may be used as the basis for the numerical evaluation of sets of Fourier coefficients. The organization of such a calculation is described, and discussed in the context of a broad comparison between this approach and various other standard methods.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 101-135
  • MSC: Primary 65.90
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0260230-8
  • MathSciNet review: 0260230