If we define c 0 = a 0 / 2 , {\displaystyle c_{0}=a_{0}/2,} c n = ( a n − i b ) / 2 , {\displaystyle c_{n}=(a_{n}-ib)/2,} and c − n = ( a n + i b ) / 2 , {\displaystyle c_{-n}=(a_{n}+ib)/2,} then we may write the complex form of the Fourier Series
