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Experimental computation with oscillatory integrals

Bailey, David H. and Borwein, Jonathan M. (2010) Experimental computation with oscillatory integrals. Contemporary Mathematics, 517 .

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    Abstract

    A previous study by one of the present authors, together with D. Borwein and I. E. Leonard 8, studied the asymptotic behavior of the p-norm of the sine function: sinc(x) = (sinx)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high precision, both as a challenge in itself, and also in an attempt to recognize the numerical values as closed-form constants. With this approach, we are able to reproduce several of the results of 8 and to find new results, both numeric and analytic, that go beyond the previous study.

    Item Type: Article
    Uncontrolled Keywords: experimental computation, oscillatory integrals, mathematics, numerical values
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 04 Sep 2013 16:30
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1219

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