Fast computation of Goursat’s infinite integral with very high accuracy

• Ooura, Takuya

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.

Journal

• Journal of Computational and Applied Mathematics

  Journal of Computational and Applied Mathematics 249 1-8, 2013-09

  Elsevier B.V.

Keywords

• Numerical quadrature
• Multiple-precision computation
• Double exponential quadrature method
• Computational complexity

Details

• CRID: 1050845760697432576
• NII Article ID: 120005244245
• NII Book ID: AA00696002
• ISSN: 03770427
• HANDLE: 2433/173114
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles