• To: mathgroup at smc.vnet.net
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 5 May 2001 04:00:41 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <9ctbb7\$m4s@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

can you please look at the manual to see that T_0 is a pattern
that never matches and iwT is a single symbol and not I*w*T and
find out that Sqrt[-1] is denoted by I and not by i ?

If you know all that you can type

Y = Integrate[Exp[-T^2/(2T0^2)]Exp[I*w*T], {T, -Infinity, Infinity},
Assumptions -> {Element[{T0, w}, Reals] && T0 > 0}]

and get

(Sqrt[2*Pi]*T0)/E^((T0^2*w^2)/2)

Regards
Jens

Rex wrote:
>
> Dear Sir,
>   I wonder why I can't get the analytic form of the following integration by Mathematica:
>   In[1] = Y=Integrate[Exp[-T^2/(2T_0^2)]Exp[iwT], {T, -Infinity,
>   Infinity}]
>   In[2] = Integrate[YExp[beta2*w^2*z-iwT],{w,-Infinity,Infinity}]
>   Unforunately, the anwser given by Mathematica is the orginal formula
>   I input.
>   Would you please give me a hand?
>
> _____________________________________________