Further asymptotic expansions for the error functional
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- by B. W. Ninham and J. N. Lyness PDF
- Math. Comp. 23 (1969), 71-83 Request permission
Abstract:
The generalised Euler-Maclaurin summation formula for the error functional $Ef = Rf - If$ is not suitable for numerical computation if $f(x)$ contains singularities in the complex plane which lie close to the interval of integration. In this paper, we use the methods and results of an earlier paper to construct alternative asymptotic expansions suitable in such cases.References
- J. N. Lyness and B. W. Ninham, Numerical quadrature and asymptotic expansions, Math. Comp. 21 (1967), 162–178. MR 225488, DOI 10.1090/S0025-5718-1967-0225488-X A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953. MR 15, 419. A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954, p. 310. MR 15, 868.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 71-83
- MSC: Primary 65.25
- DOI: https://doi.org/10.1090/S0025-5718-1969-0242351-0
- MathSciNet review: 0242351