Re: Integrate: Assumptions in double integral

• To: mathgroup at smc.vnet.net
• Subject: [mg81492] Re: Integrate: Assumptions in double integral
• From: Bhuvanesh <BhuvaneshBhatt at gmail.com>
• Date: Wed, 26 Sep 2007 06:33:04 -0400 (EDT)

```It seems to work fine for me in V6.0.1. Note that I have made the substitutions {i*wa->I*wa, iwb->I*wb} and used square brackets for Exp. Also, your variables of integration were in the opposite order.

In[1]:= Integrate[Exp[-a*ta-b*tb+I*wa*ta+I*wb*tb], {tb,0,Infinity}, {ta,0,tb}] //InputForm

Out[1]//InputForm=
If[Im[wb] + Re[b] > 0 && Im[wa + wb] + Re[a + b] > 0, 1/((b - I*wb)*(a + b - I*(wa + wb))),
Integrate[E^(a*tb - tb*(a + b - I*wb))/(a - I*wa) - E^(I*tb*wa - tb*(a + b - I*wb))/(a - I*wa),
{tb, 0, Infinity}, Assumptions -> Re[b] <= -Im[wb] || (Re[b] > -Im[wb] && Re[a + b] <= -Im[wa + wb])]]

In[2]:= Integrate[Exp[-a*ta-b*tb+I*wa*ta+I*wb*tb], {tb,0,Infinity}, {ta,0,tb}, Assumptions->{a>0,b>0,wa>0,wb>0}] //InputForm

Out[2]//InputForm= 1/((b - I*wb)*(a + b - I*(wa + wb)))

Bhuvanesh,
Wolfram Research

```

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