The Gram-Schmidt process for constructing an orthogonal set that was discussed in

Chapter 12, Problem 22

(choose chapter or problem)

The Gram-Schmidt process for constructing an orthogonal set that was discussed in Section 7. 7 carries over to a linearly independent set {f0(x),f1(x),f2(x), ... }of real-valued functions continuous on an interval [a, b]. With the inner product Un. cl>n) = s:fnix) dx, define the functions in the set B' = {c/>0(x), cf>i(x), c/>2(x), ... } to be c/>o(x) = fo(x) and so on. (a) Write out cp 3(x) in the set. (b) By construction, the setB' = {c/>0(x), c/>1(x),c/>2(x), ... }is orthogonal on [a, b]. Demonstrate that cp0(x ), c/>1 (x ), and c/>2(x) are mutually orthogonal.