Puiseux and Taylor Series of the Einstein Functions and Their Role in the Solution of Inhomogeneous Airy’s Equation

Abstract

The Einstein functions in generalized Puiseux and Taylor series are used as forcing functions in Airy’s inhomogeneous equation, and particular and general solutions are obtained. Comparison are made with solutions obtained using the Nield-Kuznetsov functions’ approach. For each of the Einstein’s functions, the standard Nield-Kuznetsov function of the second kind is expressed in terms of Bessel functions. Computations and graphs in this work were produced using Wolfram Alpha.