A survey of the use of Chebyshev polynomials in the computation and the inversion of integral transforms and in the solution of integral equations is presented. It focused on the problems showing singularity.
Piessens, R. (2000). Computing integral transforms and solving integral equations using Chebyshev polynomial approximations. Journal of Computational and Applied Mathematics, 121(1), 113–124. https://doi.org/10.1016/S0377-0427(00)00349-6