In Exercises 5–14, the space is with the inner
Chapter 6, Problem 14E(choose chapter or problem)
In Exercises 5–14, the space is \(C[0,2 \pi]\) with the inner product (6).
Suppose the first few Fourier coefficients of some function f in \(C[0,2 \pi]\) are \(a_{0}, a_{1}, a_{2}, \text { and } b_{1}, b_{2}, b_{3}\). Which of the following trigonometric polynomials is closer to f ? Defend your answer.
\(g(t)=\frac{a_{0}}{2}+a_{1} \cos t+a_{2} \cos 2 t+b_{1} \sin t\)
\(h(t)=\frac{a_{0}}{2}+a_{1} \cos t+a_{2} \cos 2 t+b_{1} \sin t+b_{2} \sin 2 t\)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer