MATH 2243 Lecture Notes - Lecture 1: Regular Singular Point
Document Summary
Usually, x0 is chosen to be a value from initial conditions when ivp. We need to classify the point x0, to determine the type of series solution to use. If p,q, are analytic at x0 (taylor series with nonzero radius of convergence rho), then x0 is called an ordinary point. If x0 is not ordinary, it is singular. If x0 is not regular singular, it is irregular singular. So x0=-2 is an irregular singular point (cannot study with tools in this class) Manipulate using steps 0-3, to get a recursion relation. For this to be true for all x, coefficients of powers of x must be zero. We want to find patterns in recursion relations, if possible. If you can"t find the pattern, truncate at some m, and you"ll have an approximation to the solution. The two solutions are analytic at x=0. x=0 is an ordinary point. Recursion relation, solve for a2 a0 and a1 are arbitrary.
