An extension of the finite Hankel transform
type: Item
instance of: scholarly article
title: An extension of the finite Hankel transform
zbMATH Open document ID: 1055.44005
DOI: 10.1016/S0096-3003(03)00372-2
author: M. Shawkey
author: Nabil T. M. El-Dabe
author: Moustafa El-Shahed
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: Integral transforms have been used extensively to solve certain class of initial and boundary value problems. \textit{I. Ali} and the reviewer [J. Aust. Math. Soc., Ser. B 41, 105--117 (1999; Zbl 0982.44003)] introduced a generalized form of the Hankel transform and applied it to the problem of a heavy pollutant from a ground level aerial source within the framework of diffusion theory. Recently, \textit{H. G. Khajah} [Integral Transforms and Spec. Funct. 14, No. 5, 403--412 (2003; Zbl 1049.44005)] considered a modified form of a finite Hankel transform. In this paper, the authors consider a generalized finite Hankel transform involving Bessel functions as kernel. Several properties including an inversion formula are given. This transform is suitable for solving certain class of mixed boundary value problems. A problem involving the flow through concentric cylinders when one of the cylinders starts rotating impulsively with a uniform angular velocity, while the other is kept fixed is solved by the use of this transform.
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 2082084
zbMATH Keywords: Bessel functions
zbMATH Keywords: operational calculus
zbMATH Keywords: finite integrals
zbMATH Keywords: inversion formula
zbMATH Keywords: mixed boundary value problems
reviewed by: S. L. Kalla
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2082084