Science:Math Exam Resources/Courses/MATH307/April 2009/Question 05 (b)
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Question 05 (b) 

5. The function for x [0, 1] can be expanded in a Fourier series = (b)[this part should worth 7 points] Suppose (x), (x), (x),... is an infinite orthonormal basis of functions on the interval [0,1] and we have the expansion
Suppose, in addition, that is the constant function (x) = 1. Is it true that = , where is the Fourier coefficient above? Give a reason. 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2009/Question 05 (b)/Hint 1 
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Solution 

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, we must have . 