An extension of the finite Hankel transform. (English) Zbl 1055.44005

Integral transforms have been used extensively to solve certain class of initial and boundary value problems. 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, 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.


44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A20 Integral transforms of special functions
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
Full Text: DOI


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