Frobenius Method

In mathematics, the Frobenius method, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form

with

and

in the vicinity of the regular singular point z=0. We can divide by z2 to obtain a differential equation of the form

which will not be solvable with regular power series methods if either p(z)/z or q(z)/z2 are not analytic at z = 0. The Frobenius method enables us to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist (and are finite).