About Calculation of the Hankel Transform Using Preliminary Wavelet Transform

The purpose of this paper is to present an algorithm for evaluating Han-kel 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 by the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates the proposed algorithm. The Hankel transform is a very useful instrument in a wide range of physical problems which have an axial symmetry [5]. The influence of the Laplacian on a function in a cylindrical coordinates is equal to the product of the squared parameter of the transformation and the transform of the function d 2 dr 2 + 1 r d dr f(r) ←→ −p 2 F 0 (p), d 2 dr 2 + 1 r d dr − 1 r 2 f(r) ←→ −p 2 F 1 (p). The Hankel transforms of the null (n = 0) and the first (n = 1) kind are represented as F n (p) = ∞ 0 f(r)J n (pr)r dr, f n (p) = ∞ 0 F(p)J n (pr)p dp.