The Hankel transform
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چکیده
منابع مشابه
Bounding Functions Via n-th Order Hankel Transform
In this presentation we establish new bounds on functions, which have their n-th order Hankel Transform bandlimited. This class of functions is proved to be also Fourier Transform bandlimited. N-th order Hankel Transforms and the consequent bounds are important for the reconstruction in CAT, MRI (Magnetic Resonance Imaging) etc. Indeed many algorithms of modern tomography use the appropriate fo...
متن کاملUsing Wavelets Based on B-splines for Calculation of the Hankel Transform
The purpose of this paper is to represent the integral Hankel transform as a series. If one uses Bspline wavelet this series is a linear combination of the hypergeometrical functions. Numerical evaluation of the test function with known analytical Hankel transform of the null kind illustrates the proposed results. Key-Words: the Hankel transform, hypergeometrical function, B-spline wavelet.
متن کاملSome conjectures on the ratio of Hankel transforms for sequences and series reversion
The Hankel transform for sequences (defined below) has attracted an increasing amount of attention in recent years. The paper [4] situated its study within the mainstream of research into integer sequences, while papers such as [2] hinted at how the study of certain Hankel transforms can lead to results concerning classical sequences. That paper exploited a link between continued fractions and ...
متن کاملThe Hankel Transform and Some of its Properties
The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also ...
متن کاملO ct 2 00 2 About calculation of the Hankel transform using preliminary wavelet transform
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied to the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates proposed algorithm. The Ha...
متن کاملInternational Conference on
The Hankel transform of an integer sequence (an) is defined as a sequence formed by the determinants of the matrices An, where An is the upper-left submatrix of size n× n of the Hankel matrix A = a0 a1 a2 a3 · · · a1 a2 a3 a4 · · · a2 a3 a4 a5 · · · .. .. .. .. . . . . In this talk, methods in deriving the Hankel transform of Bell and other Bell-type numbers will be discussed, particu...
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