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Computing integrals of highly oscillating special functions using complex integration methods and Gaussian quadratures. (English) Zbl 1372.65071

Summary: An account on computation of integrals of highly oscillatory functions based on the so-called complex integration methods is presented. Beside the basic idea of this approach some applications in computation of Fourier and Bessel transformations are given. Also, Gaussian quadrature formulas with a modified Hermite weight are considered, including some numerical examples.

MSC:

65D30 Numerical integration
41A55 Approximate quadratures
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