Abstract. In a study of the screening properties of a charged impurity located inside and near the surface of a metal subjected to a magnetic field, there arose an interesting class of Eulerian integrals, involving the Bessel function J_v(z) or J₀(z), which were expressed in closed forms by Glasser (1984). Subsequently, Wille (1988) generalized and extended Glasser's work by giving closed-form expressions for a number of Eulerian integrals involving Meijer's G-function. Motivated by these works, the authors aim at evaluating a general class of Eulerian integrals involving Fox's H-function. Their main result is shown to provide a key formula from which one can deduce each of the aforementioned integrals and also numerous other potentially useful results not contained in the earlier works; they are led, in this way, to the corrected version of one of Wille's main integral formulae.

Print publication: Issue 3 (7 February 1993)