1. See worked Griffiths example 3.8.
2. See worked Griffiths example 3.9.
3. (Ben) We write as the sum (noting that only terms with are required to represent a second order polynomial.) We find the coefficients by
   1. eyeballing: the term comes only from . Since has coefficient 3, must be 2. So now we have

      

      But , so we have exactly , giving

      

   2. The orthogonality relations 3.68 tell us that if

      

      then

      

      Since is of degree 2, vanishes for l;SPMgt;2, from

      

      We thus must find and by integration. They are

      

      Here we have used the fact that in evaluating

      

      even terms in f(x) cancel between the endpoints, while odd terms are twice the contribution from x=1.

4. See Boas section 13.5.

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