54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < 1, show that Fel8" (=)) = }(-1)" f' () – f' () – (4)* F. (n) . [(-1)" f' (1) – f' (0)] – (4) Fe (n). When l = T, show that Fe(f" (2)] = [(-1)" f' (7) – f' (0)] – 1²F. (n). [(-1)" f' (71) – f' (0)] – n²Fe (n) .
54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < 1, show that Fel8" (=)) = }(-1)" f' () – f' () – (4)* F. (n) . [(-1)" f' (1) – f' (0)] – (4) Fe (n). When l = T, show that Fe(f" (2)] = [(-1)" f' (7) – f' (0)] – 1²F. (n). [(-1)" f' (71) – f' (0)] – n²Fe (n) .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < l, show
that
2
Felf" (x)] = [(-1)" f' (1) – f' (0)] – (4)* . (n).
%3D
When l = T, show that
FelS" (12)) = [(-1)" s'(7) – f' (0)] – n°F (n).
[(-1)" f' (7) – f' (0)] – n²Fc (n).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98f82694-6c80-43d5-aeb6-1718750fc31d%2Ffefb5003-2aeb-4370-8815-863374ec463f%2F76g4l5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < l, show
that
2
Felf" (x)] = [(-1)" f' (1) – f' (0)] – (4)* . (n).
%3D
When l = T, show that
FelS" (12)) = [(-1)" s'(7) – f' (0)] – n°F (n).
[(-1)" f' (7) – f' (0)] – n²Fc (n).
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