The Fourier Coeficients of the Function $f ( x ) = x ^ { 2 }$

question 12

Multiple Choice

The Fourier coeficients of the function $f ( x ) = x ^ { 2 }$ on $[ - 1,1 ]$ are Select all that apply.

• A) \(a _ { 0 } = 2 / 3\)
• B) \(a _ { n } = 0\)
• C) \(a _ { n } = 4 ( - 1 ) ^ { n } / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• D) \(b _ { n } = 0\)
• E) \(b _ { n } = 4 ( - 1 ) ^ { n } / \left( n ^ { 2 } \pi ^ { 2 } \right)\)

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