# A modified finite Hankel transform

**ABSTRACT** A modified Hankel transform in the form [Formula: See Text] is introduced, where f(z) satisfies Dirichlet's conditions in the interval [0, b]. This transform is treated under two assumptions on the parameter s: (i) where s is a root of the transcendental equation J μ(b u) = 0, and (ii) where s is a root of the transcendental equation u J′μ(b u) + h J μ(b u) = 0 for a positive constant h. In each case, we derive the inversion formulas, Parseval-type identities, transforms of derivatives, as well as transforms of products of the form z δ f(z). Some special cases are given together with the transform of a differential operator. Our results are consistent with those established for λ = 1.

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**ABSTRACT:**This paper deals with an extension of integral transform, involving Bessel functions as kernel. The inversion formula is established and some properties are given. The transform can be used to solve certain class of mixed boundary value problems. We consider the motion of an incompressible viscous fluid in an infinite right circular cylinder rotating about its axis as an application of this generalized finite Hankel transform.Applied Mathematics and Computation 07/2007; 190(1):705-711. DOI:10.1016/j.amc.2007.01.076 · 1.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The authors define and study a Hankel-type integral transform involving the product of Bessel functions as the kernel. Relying on the Sturm-Liouville theory, they derive the inversion formula and state some properties. The authors use this transform to solve the heat conduction problem in an infinite and a semi-infinite circular cylinder, bounded by surfaces r=a and r=b (b>a), with radiation-type boundary conditions on both surfaces.01/2004; 28. - [Show abstract] [Hide abstract]

**ABSTRACT:**The theory of Sturm-Liouville finite transforms is used to obtain a general form of the finite Hankel transform in the interval [a,b]. Different transforms are obtained, as particular cases. Finally, one of this transforms is applied to solve a boundary value problem.Revista Técnica de la Facultad de Ingeniería Universidad del Zulia 01/2008; · 0.05 Impact Factor