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