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

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) $b _ { n } = 4 ( - 1 ) ^ { n } / \left( n ^ { 2 } \pi ^ { 2 } \right)$