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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • MathSciNet review: 0290020