6: Series Solutions
( \newcommand{\kernel}{\mathrm{null}\,}\)
We consider the homogeneous linear second-order differential equation for y=y(x): P(x)y″+Q(x)y′+R(x)y=0,
where P(x), Q(x) and R(x) are polynomials or convergent power series around x=x0, with no common polynomial factors that could be divided out. The value x=x0 is called an ordinary point of (???) if P(x0)≠0, and is called a singular point if P(x0)=0. Singular points will later be further classified as regular singular points and irregular singular points. Our goal is to find two independent solutions of (???).