Results 161 to 170 of about 734,785 (209)

On a generalized finite Hankel transform

Applied Mathematics and Computation, 2007
The authors introduce a new form of finite integral transform involving Bessel functions, which can be considered a generalized Hankel transform. These results are then used to solve heat conduction problems in a finite, semi-infinite and infinite cylinder along with initial and boundary conditions.
Mridula Garg, Alka Rao, Shyam L. Kalla
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Parseval's Theorem for Hankel Transforms

Proceedings of the London Mathematical Society, 1939
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On the Generalized Hankel and K Transformations

Canadian Mathematical Bulletin, 1969
The K transformation (also called the Meijer transformation) has been extended by Zemanian [1; 2] to a class of generalized functions, For , he defined the K transform of f by(1)In [2, Section 6.6] the following inversion theorem for the K transform of f is proven:(2)in the sense of weak convergence in D'(I).
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Uncertainty Inequalities for Hankel Transforms

SIAM Journal on Mathematical Analysis, 1971
In 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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The Hankel Transform

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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Fast Hankel transform algorithm

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985
The 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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A quadrature formula for the Hankel transform

Numerical Algorithms, 1995
Quadrature formulas for the integral transform to be composed by two Hankel transforms and for the closely related Hankel transform are presented, the error produced by this algorithm for a class of piecewise continuous functions is estimated and some numerical examples are listed.
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On Polyconvolutions Generated by the Hankel Transform

Mathematical Notes, 2004
The author introduces the so-called polyconvolution operators, which are associated with the Hankel transform. The existence and factorization properties for these generalized convolutions are proved. It involves Hankel's transforms of different order. By using the differential properties for the Hankel transform the author constructs more convolutions
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Hankel Transform

2023
Sudeshna Banerjea, Birendra Nath Mandal
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Quasi fast Hankel transform

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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