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http://bura.brunel.ac.uk/handle/2438/6544
Title: | The method of finite-product extraction and an application to Wiener-Hopf theory |
Authors: | Rawlins, AD |
Keywords: | Transcendental equations;Roots;Zeros;Bessel functions;Polynomial approximations;Wiener-Hopf factorization |
Issue Date: | 2011 |
Publisher: | Oxford University Press on behalf of the Institute of Mathematics and its Applications |
Citation: | IMA Journal of Applied Mathematics, Accepted for publication on 20 Jun 2011 |
Abstract: | In this work we describe a simple method for finding approximate representations for special functions which are entire transcendental functions that can be represented by infinite products. This method replaces the infinite product by a finite polynomial and Gamma functions. This approximate representation is shown in the case of Bessel functions to be very accurate over a large range of parameter values. These approximate expressions can be useful for finding the roots of a transcendental equation and the Wiener-Hopf factorization of functions involving such Bessel functions.The method is shown to be potentially useful for other transcendental andWiener-Hopf problems, which involve other entire functions that have infinite product representations. |
Description: | Copyright @ The Author, 2011. The publisher version of the article can be accessed at the link below. |
URI: | http://imamat.oxfordjournals.org/content/early/2011/07/26/imamat.hxr043.short?rss=1 http://bura.brunel.ac.uk/handle/2438/6544 |
DOI: | http://dx.doi.org/10.1093/imamat/hxr043 |
ISSN: | 0272-4979 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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