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, Parsevaltype 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.

 "It is given in the form H t ½f ðtÞ; k ¼ Z b a tf ðtÞJ t ðtkÞdt; where f(t) is a function defined in a finite interval ½a; b, satisfying the Dirichlet's conditions and J t is the Bessel function of first kind and of order t. Furthermore, Khajah [12] has studied a modified form of Hankel transform under two assumptions on the parameter. In each case the inversion formula, Parsevaltype identity, transform of derivatives and transforms of products of the kind t k f ðtÞ has been derived. "
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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):705711. DOI:10.1016/j.amc.2007.01.076 · 1.55 Impact Factor  [Show abstract] [Hide abstract]
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