Evaluation of a certain class of Eulerian integrals

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 Jv(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.