Exercises and Problems in Mathematical Methods of Physics by Giampaolo Cicogna

Author:Giampaolo Cicogna
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(3.29)

(1) The Fourier transform of the function

can be evaluated by integration in the complex plane using (with some care) Jordan lemma. Here, two alternative ways are proposed:

(a) put and evaluate first ; notice on the other hand that , which gives (one constant must then be fixed ..., recall that must belong to );

(b) write

and use .

(2) The same for the function

(a) with as before, now (two constants must be fixed to determine ..., recall that as before must belong to );

(b) write

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