Eldabe, N. T.; El-Shahed, M.; Shawkey, M. An extension of the finite Hankel transform. (English) Zbl 1055.44005 Appl. Math. Comput. 151, No. 3, 713-717 (2004). 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. Reviewer: S. L. Kalla (Kuwait) Cited in 8 Documents 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 Keywords:Bessel functions; operational calculus; finite integrals; inversion formula; mixed boundary value problems Citations:Zbl 0982.44003; Zbl 1049.44005 PDFBibTeX XMLCite \textit{N. T. Eldabe} et al., Appl. Math. Comput. 151, No. 3, 713--717 (2004; Zbl 1055.44005) Full Text: DOI 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: McGraw-Hill New York · Zbl 0265.73085 [9] Tranter, C. J., Legendre transforms, Quart. J. Math., 2, 1-8 (1952) · Zbl 0036.07401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.