indicial equation

The quadratic in r that a Frobenius series' lowest-order term forces, whose roots are the series' possible starting exponents.

Substituting the Frobenius trial $y=x^r\sum_{n=0}^{\infty}a_nx^n$ into an equation with a regular singular point at $0$ and collecting the lowest surviving power $x^r$ produces the indicial equation $r(r-1)+p_0r+q_0=0$ , whose two roots $r_1,r_2$ are the only exponents a Frobenius series solution can start at.