Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639337 | Journal of Computational and Applied Mathematics | 2013 | 8 Pages |
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
Authors
Takuya Ooura,