What is the complex Fourier series of the function f(t) = cos t? Hint: if you're confident, you can do this without integrating anything. O jet + 1e-it О 1 2 it Σ 2n(-1)" 1 cint 2° n² - 1 n=-00, n#1 00 2n(-1)7+1 -eint n² – 1 1 Σ n=-00, n+±1 Σ 2n(-1)" eint n² – 1 1+ n=-00, n#0 O None of these. +

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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What is the complex Fourier series of the function f(t) = cos t?
Hint: if you're confident, you can do this without integrating anything.
1e-it
get + je it
O 1
oit
2n(-1)" cint
n² –1
1
2
n=-00, n+±1
2n(-1)** int
Σ
1
eit +e it+
|
n2 –1
n=-00, n+±1
2n(-1)" cint
00
1
1+
Σ
n2 – 1
n=-00, n#0
O None of these.
it
Transcribed Image Text:What is the complex Fourier series of the function f(t) = cos t? Hint: if you're confident, you can do this without integrating anything. 1e-it get + je it O 1 oit 2n(-1)" cint n² –1 1 2 n=-00, n+±1 2n(-1)** int Σ 1 eit +e it+ | n2 –1 n=-00, n+±1 2n(-1)" cint 00 1 1+ Σ n2 – 1 n=-00, n#0 O None of these. it
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