Unformatted text preview: f ( x ) = ∞ X ´ a n cos nx √ π + b n sin nx √ π µ . a . (5) Find the value of a n for each n . (Hint: Use the scalar product. What is the integral of an odd function on the given interval?) b . (5) Find the value of b n for each n . (Hint: Use the scalar product.) c . (10 bonus points!) Use the results of (a) and (b) together with the Plancherel Identity to ±nd the numerical value of ∞ X 1 1 n 2 . (The bonus points will be based on the correctness of your calculation— not on looking up the answer.) 1...
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This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.
- Summer '08