Let me rewrite what I wrote in last post again, since it did not
format well.
I think it does converge.
int( exp(-I 2 Pi f t),{t,0,infinity) =
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi f t) }
0
Let f be complex in general, say (a+ I b) then the above becomes
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi (a +I b) t) }
0
or
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi a t) exp (2 Pi b t) }
0
Since b<0 (this is the assumption that Im(f)<0 ), then the above
becomes
1/(-I 2 Pi f) * [ 0 - 1 }
or
1/(I 2 Pi f)
or
-I/(2 Pi f)
Nasser
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