MATH 2243 Lecture Notes - Lecture 1: Divergent Series, Ordinary Differential Equation, Paten
Document Summary
Every power series has a radius and an interval of convergence. In de, we only care about radius of convergence, if we care at all. If rho=0, the series only converges at x=x0, i. e. a divergent series. In calculus, you get rho using the ratio test. Inside the radius of convergent, the power series is equal to a function. A function f with taylor series about x=x0 with nonzero radius of convergence rho>0 is said to be analytic at x=x0. Need to know an in terms of n (found the paten) in. Find the radius of convergence by finding distance to nearest complex pole! Find the radius of convergence of series expansion of. Taylor expand about x0 any functions in front of your series. Multiply through by any (x-x0) not in your series. (must be expanded about same point. Start each summation at same value of n.
