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Title: Fast computation of Goursat’s infinite integral with very high accuracy
Authors: Ooura, Takuya  kyouindb  KAKEN_id
Author's alias: 大浦, 拓哉
Keywords: Numerical quadrature
Multiple-precision computation
Double exponential quadrature method
Computational complexity
Issue Date: Sep-2013
Publisher: Elsevier B.V.
Journal title: Journal of Computational and Applied Mathematics
Volume: 249
Start page: 1
End page: 8
Abstract: We propose an efficient computation method for the infinite integral View the MathML source, whose integrand contains a series of spikes, approximately π apart, growing taller and narrower as x 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.
Rights: © 2013 Elsevier B.V.
This is not the published version. Please cite only the published version.
DOI(Published Version): 10.1016/
Appears in Collections:Journal Articles

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