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...

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...

we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our 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.

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 ...

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure, not requiring exponential sampling, is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into...

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 ...

Postnicov [22], in 2003, proposed an algorithm to compute the Hankel transforms of order zero and one by using Haar wavelets. But the proposed method faced problems in the evaluation of zero order Hankel transform. The purpose of this paper is to overcome this problem and obtain an efficient algorithm for evaluating Hankel transform of order zero by using rationalized Haar wavelets. Exact analy...

The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind to the series of the Bessel function for Hankel transform of the first kind and Bessel and Struve function for Hankel transform of the null kind multiplied to the wavelet coefficients of the input function. It is both the exact analytical representation and the base for effective ...