Generalized finite Hankel transform
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.
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ABSTRACT: The numerical projection method for the zero-order Hankel transform inversion for the case of data given on a finite interval has been developed. The justification of the convergence of the projection method has been done for the general case that also includes the sine-Fourier transform inversion. An inequality on the norms of the zeroth-order Laguerre functions has been proved. The efficiency of the method was illustrated with the test data and for the problem of cylindrical distribution function calculation using the melt surface layer diffraction data.Integral Transforms and Special Functions 06/2011; 22(6-6):431-441. DOI:10.1080/10652469.2010.518568 · 0.72 Impact Factor