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Delta function in r Delta function in k 1 Exponential in 8(2) 1 2πδ(k) 2a a²+k² (a>0)

Delta function in r Delta function in k 1 Exponential in 8(2) 1 2πδ(k) 2a a²+k² (a>0)

Advanced Engineering Mathematics
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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1) Derive the Fourier transform of functions Description Delta function in x Delta function in k Exponential in Exponential in k Gaussian Function 8(x) 1 Transform 1 2πδ(k) (a > 0) 2a a²+k² 2πe-alk (a>0) √2πe-k²/2
Transcribed Image Text:1) Derive the Fourier transform of functions Description Delta function in x Delta function in k Exponential in Exponential in k Gaussian Function 8(x) 1 Transform 1 2πδ(k) (a > 0) 2a a²+k² 2πe-alk (a>0) √2πe-k²/2
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