Suppose that it is desired to construct a set of
Chapter 11, Problem 9(choose chapter or problem)
Suppose that it is desired to construct a set of polynomials P0(x), P1(x), ... , Pk(x), ... ,where Pk(x) is of degree k, that are orthogonal on the interval 1 x 1; see 7. Suppose further that Pk(x) is normalized by the condition Pk(1) = 1. Find P0(x), P1(x),P2(x), and P3(x). Note that these are the first four Legendre polynomials (see of Section 5.3).(b) Show that ni=1a2i 10r(x)f 2(x) dx. This result is known as Bessels inequality.(c) Show that i=1a2i converges.(d) Show that limn Rn =10r(x)f 2(x) dx i=1a2i .(e) Show that i=1aii(x) converges to f(x) in the mean if and only if10r(x)f 2(x) dx = i=1a2i .This result is known as Parsevals equation.I
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