An extension of the finite Hankel transform
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.
scientific article; zbMATH DE number 2082084