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

Multiple Choice

The Fourier series of the function $f ( x ) = x ^ { 2 }$ on $[ - 1,1 ]$ is

A) $\sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right) + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)$
B) $\sum _ { n = 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)$
C) $\sum _ { n = 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)$
D) $1 / 3 + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)$
E) $1 / 3 + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)$