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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.
ISSN: 0272-4979
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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