Thread: Problem 32
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Old August 2nd, 2007, 12:24 PM
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Originally Posted by Rebesques View Post
I claim this is cheating!

Since, by identifying a Sturm-Liouville operator here, the P_n(x) are eigenvectors and thus orthogonal for the L^2 inner product - that is, \int_{-1}P_n(x)P_m(x) dx = 0; qed!
Yes, that is cheating. It takes all the fun away from the problem if it can be done.*

(Change "eigenvectors" to "eigenfunctions" to fix your post.)


*)I say "if it can be done" because this is not a boundary value problem. Thus, Sturm-Louiville Theory does not apply. Are you sure?
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