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Integrate: Assumptions in double integral


Hi!

Suppose that I have an integral (integration over damped wave in two
dimensions)

Integrate[Exp(-a*ta-b*tb+i*wa*ta+iwb*tb),{ta,0,tb},{tb,0,infinity}]

Why does it not matter, whether I include assumptions
(Assumptions->{a>0,b>0,wa>0,wb>0}) or not, i.e. in both cases, I get the
same result (an conditional in dependence of real and imaginary part of
the variables). In other words, it does not seem as if Mathematica 6
recognizes the conditions for a,b,wa,wb. On the other hand, if I compute
the integral in a nested scheme

Integrate[Integrate[...,{ta,0,tb},Assumptions],{tb,0,infinity}]

I get a Lorentzian function. Why is this so?
In this spirit
With thanks for your efforts
Yours Gernot


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