Ascending Series Solution to Airy's Inhomogeneous Boundary Value Problem

Abstract

A two-point boundary value problem involving the nonhomogeneous differential equation of Sir George Biddell Airy with a right-hand-side that is a function of the independent variable, is considered. Solution is expressed in terms of two recently introduced integral functions that are expressible in terms of ascending series. Evaluation of these functions gives rise to an open problem that is stated in this work.