MATH307 December 2012
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Question 04 (b)
Consider the Fourier series
(b) The coefficient cn can be written as an inner product . What are ƒ and g?
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To compute the coefficient, start with
where and . Also, we have L=1-0=1. Take the inner product of ƒ(t) with . The only term in the infinite sum that remains is the one with , and in this case . Thus
and we get the formula
Since we have , and so we overall find that
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