ABSTRACT
In the last chapter we considered Taylor series, and were able to show in some cases that the remainder Rn(x), which is just the difference between the function f(x) and its n-th order Taylor polynomial, has a limit 0 as n goes to ∞. A new problem arises when there is no known function f(x) in the background. As a concrete example, consider Airy’s differential equation
d2y
dx2 − xy = 0. (4.1)
A fruitful approach is to look for a power series solution
y(x) = ∞∑
akx k.
