Re: Integrating using If[ ]
- To: mathgroup at smc.vnet.net
- Subject: [mg33323] Re: [mg33301] Integrating using If[ ]
- From: "Philippe Dumas" <dumasphi at noos.fr>
- Date: Thu, 14 Mar 2002 19:51:26 -0500 (EST)
- References: <200203140722.CAA10975@smc.vnet.net>
- Reply-to: "Philippe Dumas" <dumasphi at noos.fr>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Michael
Try this:
x[t_] = Exp[-Abs[t]]
instead of:
If[t>=0,Exp[-t],Exp[t]];
And then you get the result with :
f[s_] = Integrate[x[t] Exp[-s t], {t, -Infinity, Infinity}]
Philippe Dumas
99, route du polygone
03 88 84 67 80
67100 Strasbourg
----- Original Message -----
From: "Michael Chang" <michael_chang86 at hotmail.com>
To: mathgroup at smc.vnet.net
Subject: [mg33323] [mg33301] Integrating using If[ ]
> Hi everyone,
>
> While recently trying out my spiffy new version of Mathematica 4.1 for
> Windoze XP, I've stumbled upon the following perplexing result.
>
> Suppose I define
>
> In[1]:= x[t_]:=If[t>=0,Exp[-t],Exp[t]];
>
> If I now try and evaluate (a two-sided Laplace Transform)
>
> In[2]:= Integrate[x[t] Exp[-s t],{t,-Infinity,Infinity}]
>
> all I get back is essentially an unevaluated answer. Replacing
> {-Infinity, Infinity} by, for instance, {-100,100}, *does* give me an
> answer, though.
>
> Typing in
>
> In[3]:= Integrate[Exp[-Abs[t]] Exp[-s t],{t,-Infinity,Infinity}]
>
> however, does give me back a meaningful result with the conditionals
> properly stated that -1<Re[s]<1. Why does In[3] work, but not In[1]
> and In[2]? Am I foolishly doing something stup!d here?
>
> Michael
>
>
- References:
- Integrating using If[ ]
- From: michael_chang86@hotmail.com (Michael Chang)
- Integrating using If[ ]