On the evaluation of highly oscillatory finite Hankel transform using special functions (Q285032)

The main result of this paper is a Clenshaw-Curtis-Filon-type method for the evaluation of a highly oscillatory finite Hankel transform. It is based on the Hermite interpolant at \((N + 1)\) Clenshaw-Curtis points and can be efficiently evaluated in \({\mathcal O}(N\, \log \, N)\) operations by a fast Fourier transform. An explicit expression of the modified moments is provided using the Lommel function and the Meijer G-function.The upper bound for the remainder is constructed. It is outlined that the method can be employed even for functions that has singularities at two end-points. Numerical examples demonstrate the efficiency and accuracy of the method.