Abstract
An integral equation of the Fredholm type which appears in problems of physical interest-like the dielectric response of an inhomogeneous confined quasi-tridimensional electron gas-is studied when the kernel contains an infinite number of dyadic terms. In terms of a representation, this amounts to inverting an infinite matrix. The conditions for the existence of a bound inverse are established and an explicit non-recursive algorithm is developed which can be used in practical calculations to generate successive approximations which converge to the exact answer.