Integrate: Assumptions in double integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg81438] Integrate: Assumptions in double integral*From*: Gernot Pfanner <pfannerg at no-email-reply.at>*Date*: Sun, 23 Sep 2007 04:35:52 -0400 (EDT)

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