Computation of highly oscillatory Bessel transforms with algebraic singularities

Zhenhua Xu, Shuhuang Xiang

In this paper, we consider the Clenshaw-Curtis-Filon method for the highly oscillatory Bessel transform ${\int }_0^1{x}^{\alpha }(1-x{)}^{\beta }f(x)J_{\nu }(\omega x)dx$, where $f$ is a smooth function on $[0, 1…