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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.

MSC:

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
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References:

[1] Ali, I.; Kalla, S., A generalized Hankel transform and its use for solving partial differential equations, J. austral. math. soc. ser. B, 41, 105-117, (1999) · Zbl 0982.44003
[2] Andrews, L.C., Special functions and of mathematics for engineers, (1998), Oxford Science Publications · Zbl 0909.33002
[3] Andrews, L.C.; Shivamoggi, B.K., Integral transforms for engineering and applied mathematicians, (1989), Oxford Science Publications · Zbl 0755.44001
[4] Cinelli, G., An extension of the finite Hankel transform and applications, Int. J. eng. sci., 3, 539-559, (1965) · Zbl 0151.17102
[5] Kalla, S., On a new integral transform. I, Jnanabha, 9-10, 149-154, (1980) · Zbl 0507.44002
[6] Nanda, I.N., Unsteady circulatory flow about a circular cylinder with suction, Appl. sci. res., 9, 85-92, (1962) · Zbl 0091.42201
[7] Sneddon, I.N., On finite Hankel transform, Philos. mag., 37, 17-25, (1946) · Zbl 0063.07107
[8] Sneddon, I.N., The use of integral transform, (1972), McGraw-Hill New York · Zbl 0265.73085
[9] Tranter, C.J., Legendre transforms, Quart. J. math., 2, 1-8, (1952) · Zbl 0036.07401
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