As we know, if the equation $$a(x)y''+b(x)y'+c(x)=0 \ \ \ \ \ \ \ \ \ (1)$$
has a regular singular point at $x=x_0$ then we seek solution of the equation as
$$y(x)=\sum_{n=0}^{\infty}\beta_n (x-x_0)^{n+\lambda} \ \ \ \ \ \ \ (2)$$
but what about the case when the equation $(1)$ has several singular points? At which point should I expand (2) series ? What principle should I use to take right expansion point?