       Re: Defining function

• To: mathgroup at smc.vnet.net
• Subject: [mg44562] Re: Defining function
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Fri, 14 Nov 2003 01:58:58 -0500 (EST)
• References: <bovtvd\$nbc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Ravinder Kumar B." <ravi at crest.ernet.in> wrote:
> How to define a function over two different ranges in mathematica.
> For example
>
> f(t):= Exp[-i*t]  for t > 0   and
>      = 0          for t < 0

(This type of question seems to be asked frequently.)
The common (and perhaps best) answer would to write it using the UnitStep
function as

f[t_] := UnitStep[t]Exp[-i*t]

but that also defines f at t = 0, which perhaps you didn't want. If that is
the case, here are two other options, which leave f undefined at t = 0:

f[t_] := Which[t < 0, 0, t > 0, Exp[-i*t]]

f[t_] := (1 + Abs[t]/t)/2 * Exp[-i*t]

Note that the latter also leaves f undefined at +/-Infinity, if that's a
concern.

There are other options too.

David

```

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