A recent paper (Jokela et al 2008 Preprint arXiv:0806.1491) contains a surmise about an expectation value in a Coulomb gas which interacts with an additional charge ξ that sits at a fixed position. Here, I demonstrate the validity of the surmised expression and extend it to a certain class of higher cumulants. The calculation is based on the analogy to statistical averages in the circular unitary ensemble of random-matrix theory and exploits properties of orthogonal polynomials on the unit circle.