Thread: Problem 32
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Old August 2nd, 2007, 11:26 AM
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Quote:
The trick is to write the differencial equation as (in Sturm-Louiville form)
I claim this is cheating!

Since, by identifying a Sturm-Liouville operator here, the P_n(x) are eigenfunctions and thus orthogonal for the L^2 inner product - that is, \int_{-1}P_n(x)P_m(x) dx = 0; qed!
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Last edited by Rebesques; August 2nd, 2007 at 01:24 PM. Reason: eigenfunctions, more precisely