Regular singular point

Summary

A regular singular point of a linear differential equation is a singular point where the coefficients blow up only mildly. In the normalised equation, the coefficient of $y^{(n-k)}$ has a pole of order at most $k$ there. At such a point the solutions grow at most like a power of the distance to the point. The Frobenius method then finds solutions of the form $(z - z_0)^r$ times a power series. Bessel, Legendre and hypergeometric equations all have regular singular points. See the definition.