Re: Defining Real expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg8522] Re: [mg8494] Defining Real expressions
• From: Daniel Lichtblau <danl>
• Date: Thu, 4 Sep 1997 02:20:20 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Marco Beleggia wrote:
>
> I must evaluate an Integral in which I'd like to assign real values to
> some parameters, but I don't know how to do that.
>
> For example, in the following integral (a Fourier Transform):
>
> f[x_,p_]=Integrate[y/(x^2+y^2) Exp[-I p y],{y,-Infinity,Infinity}],
>
> p should be a real parameter. The output given by Mathematica is
> conditioned to Im[p]==0, such as If[Im[p]==0,....,....], which is not
> easy to handle, and I'd like to avoid this complication.
>
> Is it possible ?
>
> Thanks
> --
> Marco Beleggia

Maybe something along these lines?

In[29]:= Integrate[y/(x^2+y^2) Exp[-I p y],
{y,-Infinity,Infinity},
Assumptions-> Im[p]==0 && Im[x]==0]
-I Pi Sign[p]
Out[29]= -------------
2  2
Sqrt[p  x ]
E

Another possibility is to assume that the "natural" assumptions to make
are the ones you have in mind (and also that the integration code has
the same idea of "natural" as you have).

In[30]:= Integrate[y/(x^2+y^2) Exp[-I p y],
{y,-Infinity,Infinity},GenerateConditions->False]
-I Pi Sign[p]
Out[30]= -------------
2  2
Sqrt[p  x ]
E

Daniel Lichtblau
Wolfram Research
danl at wolfram.com

```

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