The document summarizes the complex form of Fourier series. It states that after substituting sine and cosine terms into the Fourier series formula, the complex form involves a summation of terms with coefficients multiplied by exponential terms with integer multiples of i and x. It provides the formulas for calculating the coefficients c0, c1, c2, etc. and gives an example function defined over an interval to demonstrate the complex form.

1. Assalamu’alaikum wr wb

2. Group 15
1. M. Derry R.A (A1C410210)
2. Hairul Akbar (A1C410211)

3. Complex Form Of Fourier Series

4. • After we substite sin nx and cos nx to fourier
series formula we can get the complex form of
fourier series is :
inx inx 2 inx 2 inx
f ( x) c0 c1 e c 1e c2e c 2e ....
1
With coefficient: c0 f ( x ) dx
2
1 inx
cn f ( x )e dx
2

5. • Example
1, x 0
f ( x) { 0,0 x

6. Other Interval
• Fuction of other interval is:

7. • With coefficient:

8. • Example
0,0 x l
f ( x) {
1, l x 2 l

9. Thank you