Exercise 7.9.14. Show that if all the roots x0 of (x) have |x0| > 1, then there

Exercise 7.9.14. Show that if all the roots x0 of Φ(x) have |x0| > 1, then there exists a polynomial

Ψ(x) =

∞Σ

i=0

ψixi with

∞Σ

i=0

|ψi| < ∞

and, for x ∈ [−1,1],

[Ψ(x)] [Φ(x)] = 1.

Hint: Do a Taylor expansion of 1/Φ(x) about 0.