Question 9 Let a not be an integer, and f (x) = cos ar, I E (-7, 7] Extend f to PC (27). (a) Compute the Fourier series of f. (b) Discuss its pointwise convergence. (c) Apply Parseval's formula to show sin 207 1+ 207 ´sin on 2 =)' - (;. 1 ' (n² – a²)² ·
Question 9 Let a not be an integer, and f (x) = cos ar, I E (-7, 7] Extend f to PC (27). (a) Compute the Fourier series of f. (b) Discuss its pointwise convergence. (c) Apply Parseval's formula to show sin 207 1+ 207 ´sin on 2 =)' - (;. 1 ' (n² – a²)² ·
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![Question 9
Let a not be an integer, and
f (r) = cos ar, r E [-7, 7]
Extend f to PC (27).
(a) Compute the Fourier series of f.
(b) Discuss its pointwise convergence.
(c) Apply Parseval's formula to show
2 00
sin an
1+
sin 207
2
a sin aT
207
( (n² – a²)² °
n=1
(d) Show that
1
cot an = -
1
απ.
n2 - a2
and
1
2
(-1)"
CSC OT = -
n2 - a2
n=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F33fabe9b-e48b-4a84-8343-a1e7c89a44bd%2Fe6h89gi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 9
Let a not be an integer, and
f (r) = cos ar, r E [-7, 7]
Extend f to PC (27).
(a) Compute the Fourier series of f.
(b) Discuss its pointwise convergence.
(c) Apply Parseval's formula to show
2 00
sin an
1+
sin 207
2
a sin aT
207
( (n² – a²)² °
n=1
(d) Show that
1
cot an = -
1
απ.
n2 - a2
and
1
2
(-1)"
CSC OT = -
n2 - a2
n=1
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