Abstract
The numerical evaluation of slowly convergent integrals with infinite limits and regularly oscillating analytic integrands is discussed. Functions are presented that can be subtracted from the integrands to increase the rate of convergence. One of the integrals used as an example is an often-studied Fourier integral related to the power spectrum of a phase-modulated wave. It is pointed out that, when Fourier integrals whose values are known to be positive, e.g., probability densities, are evaluated by the trapezoidal rule, the values given by the trapezoidal rule are never less than the true values.
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