668 FOURIER SERIES
- Sketch the waveform defined by:
f(x)=⎧
⎪⎪
⎪⎪
⎨⎪⎪
⎪⎪
⎩1 +2 x
π, when−π<x< 01 −2 x
π, when 0<x<πDetermine the Fourier series in this range.⎡⎢
⎢
⎣f(x)=8
π^2(
cosx+1
32cos 3x+1
52cos 5x+1
72cos 7x+···)⎤⎥
⎥
⎦- For the Fourier series of Problem 8, deduce a
series forπ^2[^8
π^2
8= 1 +1
32+1
52+1
72+1
92+···]