Frobenius method

Summary

The Frobenius method finds solutions of a second-order linear differential equation near a regular singular point in the form $(z - z_0)^r \sum_{k \ge 0} a_k (z - z_0)^k$. The exponent $r$ comes from a quadratic equation, the indicial equation, and the coefficients $a_k$ from a recurrence. It extends the power series method, which works only at ordinary points. It produces Bessel functions, Legendre functions and hypergeometric functions. See the definition.