       • To: mathgroup at smc.vnet.net
• Date: Sat, 5 May 2001 04:00:45 -0400 (EDT)
• References: <9ctbb7\$m4s@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You need to be careful with the syntax in Mathematica.  Some guidelines:

1. Avoid using capital letters for variables.  Mathematica often uses capital
letters for specially defined uses.

2.  You need to be aware that if you do not use a space between variables,
Mathematica sees this as one variable.  In your case "iwT" is NOT seen as i*w*T
but instead as a variable called "iwT".  You can uses spaces to indicate
multiplication "i w T" or use the multiplication sign "*", i*w*T.  I perfer the
multiplication sign since it avoids the problem of not catching a missing space.

3.  Do not use the underline character for a constant.  In your example T_0 is
causing a lot of the problem.  Mathematica will recognize things like t0 as
being different from t*0.

With these in mind try your 1st function as:

Exp[-t^2/(2*t0^2)]Exp[i*w*t] and integrate with respect to small t.  Things
should work out.

Exp[beta2*w^2*z-i*w*t
Unfortunatley, because of the limits of t there is not a closed form and
Mathematica just spits back the input.  This is Mathematica's way of saying it
does not know how to to it.  Sometimes it is possible to get an evaluation if
you manipulate the function into another form.  However, in this case:
Exp-[-i*w*t] oscillates from -1 to +1 and the integral will never converge for
+/-Infinity.

In article <9ctbb7\$m4s at smc.vnet.net>, Rex says...
>
>Dear Sir,
>  I wonder why I can't get the analytic form of the following integration by Mathematica:
>  In = Y=Integrate[Exp[-T^2/(2T_0^2)]Exp[iwT], {T, -Infinity,
>  Infinity}]
>  In = 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?
>
>_____________________________________________
>

```

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