ABSTRACT
In the treatise on ‘fluxional equations,’ Newton mentioned that all differential equations admit power series solutions. This statement influenced many mathematicians of eighteenth century including Euler. In the quest of finding the power series solutions to various ODEs, Euler introduced ‘cylindrical functions’ which were studied extensively by Bessel (we now call them as Bessel's functions). Later on, the reasons for the success as well as limitations of this method are identified. We discuss some of them in this chapter.
