Frobenius method

Seeking a series solution of the generalized form x^r times a power series, at a regular singular point.

The Frobenius method seeks a solution $y=x^r\sum_{n=0}^{\infty}a_nx^n$ ( $a_0\neq0$ ) at a regular singular point, finding the exponent $r$ from the indicial equation and the coefficients $a_n$ from the resulting recurrence relation -- generalizing the ordinary power-series method to a point where a plain series fails.