In
mathematics, in the theory of
ordinary differential equations in the complex plane ![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3804)
, the points of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3804)
are classified into
ordinary points, at which the equation's coefficients are
analytic functions, and
singular points, at which some coefficient has a
singularity. Then amongst singular points, an important distinction is made between a
regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an
irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the
hypergeometric equation, with three regular singular points, and the
Bessel equation which is in a sense a
limiting case, but where the analytic properties are substantially different.