Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)
Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)
![1 (k)
(k · k)(27)³
G(k) = 47
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3c8e58f-deba-4ecb-af4d-f4f1880bbc18%2F3a7be0d1-176e-4ca5-8931-4f838d83e005%2F4zd762g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 (k)
(k · k)(27)³
G(k) = 47
3
![1
ƒ(k) = Fx->k{f(x)} =
(2т)3
(27 )3 /e (x)e+ix* g³x,
XER3
{(x) = Fxbx{f(k)} = / š(k)e¬ix
-ix-k d³k
k-x
KER3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3c8e58f-deba-4ecb-af4d-f4f1880bbc18%2F3a7be0d1-176e-4ca5-8931-4f838d83e005%2Fq4if8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
ƒ(k) = Fx->k{f(x)} =
(2т)3
(27 )3 /e (x)e+ix* g³x,
XER3
{(x) = Fxbx{f(k)} = / š(k)e¬ix
-ix-k d³k
k-x
KER3
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