Comparison of some methods for evaluating infinite range oscillatory integrals

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Abstract

A number of related methods for the evaluation of oscillatory integrals over infinite ranges which arise in physical applications are compared critically. Various modifications are suggested and recommendations made for more efficient implementation. In particular, coefficients for Gaussian trigonometric quadrature formulas are listed and an alternative Chebyshev-polynomial-based oscillatory integrator is suggested. The use of these algorithms coupled with summation accelerators in the partition-extrapolation procedure is illustrated in a number of practical examples and comparisons are made with earlier work.

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