2022
DOI: 10.23939/mmc2022.02.241
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High accurate method to calculate a singular integral related to Hankel transform

Abstract: In this paper we are interested in the approximation of the integral \[I_0(f,\omega)=\int_0^\infty f(t)\,e^{-t}\,J_0(\omega t)\,dt\] for fairly large $\omega$ values. This singular integral comes from the Hankel transformation of order $0$, $f(x)$ is a function with which the integral is convergent. For fairly large values of $\omega$, the classical quadrature methods are not appropriate, on the other side, these methods are applicable for relatively small values of $\omega$. Moreover, all quadrature metho… Show more

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