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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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Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature
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by J. N. Lyness PDF
Math. Comp. 25 (1971), 87-104 Request permission

Abstract:

The conventional Fourier coefficient asymptotic expansion is derived by means of a specific contour integration. An adjusted expansion is obtained by deforming this contour. A corresponding adjustment to the Euler-Maclaurin expansion exists. The effect of this adjustment in the error functional for a general quadrature rule is investigated. It is the same as the effect of subtracting out a pair of complex poles from the integrand, using an unconventional subtraction function. In certain applications, the use of this subtraction function is of practical value. An incidental result is a direct proof of Erdélyi’s formula for the Fourier coefficient asymptotic expansion, valid when $f(x)$ has algebraic or logarithmic singularities, but is otherwise analytic.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 87-104
  • MSC: Primary 42.10
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0290020-2
  • MathSciNet review: 0290020