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Optics Letters, 1977
We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using
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We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using
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Positivity and Hankel transforms
Proceedings of the American Mathematical Society, 2022In this work we prove that some integrals of special functions are positive by applying the Plancherel theorem for Hankel transforms and positivity of the modified Bessel functions. We also prove that, except an extra elementary factor, Hankel transforms map subsets of completely monotonic functions into complete monotonic functions.
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Understanding fast Hankel transforms
Journal of the Optical Society of America A, 2001Recently Ferrari et al. [J. Opt. Soc. Am. A16, 2581 (1999)] presented an algorithm for the numerical evaluation of the Hankel transform of nth order. We demonstrate that this formulation can be interpreted as an application of the projection slice theorem.
Bruce W. Suter, Robert A. Hedges
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Uncertainty Inequalities for Hankel Transforms
SIAM Journal on Mathematical Analysis, 1971In this paper an uncertainty inequality for Hankel transforms is obtained.Let $\nu > 0$ be fixed. We set \[ d\mu _\nu (x) = c_\nu ^{ - 1} x^{2v} dx,\quad c_\nu = 2^{{{\nu - 1} / 2}} \Gamma (\nu + \frac{1}{2}),\] and \[ {\bf J}_\nu (x) = c_\nu x^{ - \nu + {1 / 2}} J_{\nu - {1 / 2}} (x),\] where $J_{\nu - {1 / 2}} (x)$ is a Bessel function of the first ...
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Parseval's Theorem for Hankel Transforms
Proceedings of the London Mathematical Society, 1939zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized finite Hankel transform
Integral Transforms and Special Functions, 2006This 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 ...
Moustafa El-shahed, M. Shawkey
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2009
Hankel transforms arise naturally in solving boundary-value problems formulated in cylindrical coordinates. They also occur in other applications such as determining the oscillations of a heavy chain suspended from one end, first treated by D. Bernoulli.
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Hankel transforms arise naturally in solving boundary-value problems formulated in cylindrical coordinates. They also occur in other applications such as determining the oscillations of a heavy chain suspended from one end, first treated by D. Bernoulli.
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Fast Hankel transform algorithm
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985The Hankel, or Fourier-Bessel, transform is an important computational tool for optics, acoustics, and geophysics. It may be computed by a combination of an Abel transform, which maps an axisymmetric two- dimensional function into a line integral projection, and a one- dimensional Fourier transform.
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