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Numerical evaluation of the Hankel transform by using linear Legendre multi-wavelets. (English) Zbl 1197.65237

Summary: An efficient algorithm for evaluating the Hankel transform \(F_n(p)\) of order \(n\) of a function \(f(r)\) is given. As the continuous Legendre multi-wavelets forms an orthonormal basis for \(L^{2}(\mathbb{R})\); we expand the part \(rf(r)\) of the integrand in its wavelet series reducing the Hankel transform integral as a series of Bessel functions multiplied by the wavelet coefficients of the input function. Numerical examples are given to illustrate the efficiency of the proposed method.

MSC:

65T50 Numerical methods for discrete and fast Fourier transforms
65T60 Numerical methods for wavelets
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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