The Fourier Coeficients of the Function $f ( x ) = x$

question 18

Multiple Choice

The Fourier coeficients of the function $f ( x ) = x$ on $[ - 1,1 ]$ are

• A) \(a _ { 0 } = - 2 / \pi , b _ { n } = 0 , a _ { n } = 0\)
• B) \(a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi ) , a _ { n } = 0\)
• C) \(a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi ) , a _ { n } = 0\)
• D) \(a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi )\)
• E) \(a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi )\)