Article ID Journal Published Year Pages File Type
4639337 Journal of Computational and Applied Mathematics 2013 8 Pages PDF
Abstract

We propose an efficient computation method for the infinite integral ∫0∞xdx/(1+x6sin2x), whose integrand contains a series of spikes, approximately ππ apart, growing taller and narrower as xx increases. Computing the value of this integral has been a problem since 1984. We herein demonstrate a method using the Hilbert transform for changing this type of singular function into a smooth function and computing the value of the integral to more than one million significant digits using a superconvergent double exponential quadrature method.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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