Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature

Author: J. N. Lyness
Journal: Math. Comp. 25 (1971), 87-104
MSC: Primary 42.10
MathSciNet review: 0290020
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 42.10

Retrieve articles in all journals with MSC: 42.10

Additional Information

Keywords: Fourier coefficients, Euler-Maclaurin summation formula, Fourier coefficient asymptotic expansion, numerical quadrature, subtracting out singularities
Article copyright: © Copyright 1971 American Mathematical Society