Re: Why the FourierTransform gives two different answers?

*To*: mathgroup at smc.vnet.net*Subject*: [mg125138] Re: Why the FourierTransform gives two different answers?*From*: Dana DeLouis <dana.del at gmail.com>*Date*: Thu, 23 Feb 2012 05:49:31 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> Why the FourierTransform gives two different answers? > In[1] FourierTransform[ (t - 5.0)^2*Exp[-(t - 5.0)^2 ], t, w] > In[2] FourierTransform[ (t - 5)^2* Exp[-(t - 5)^2 ], t, w] Hi. I don't have an answer, but an observation. This seems strange, and I don't really see where the machine rounding error is coming from. If we take a basic formula of the Fourier equation, then the question is why is the first part dropped to zero when done at machine precision. FullSimplify[Integrate[(t - 5)^2*Exp[-(t - 5)^2], t]] ((-(1/2))*(-5 + t))/E^(-5 + t)^2 - (1/4)*Sqrt[Pi]*Erf[5 - t] FullSimplify[Integrate[(t - 5.)^2*Exp[-(t - 5.)^2], t]] 0. - 0.44311346272637897*Erf[5. - 1.*t] The difference is this part... equ=-(1/2) E^-(-5+t)^2 (-5+t); It plots nicely: Plot[equ,{t,0,5}] It has a nice value at 4: N[equ] /.t->4 0.18394 But for some reason, simplifying it gives 0. N[equ] //FullSimplify 0. I don't have an explanation for this behavior (bug maybe??) Even if we substitute w for t-5, it still doesn't reduce to zero at full precision, and it does plot nicely. FullSimplify[((-(1/2))*w)/E^w^2] ((-(1/2))*w)/E^w^2 = = = = = = = = = = = = = = = HTH :>) Dana DeLouis Mac & Math 8 = = = = = = = = = = = = = = = On Feb 21, 6:22 am, =D0=90=D0=BB=D0=B5=D0=BA=D1=81=D0=B5=D0=B9 <avde... at gmail.com> wrote: > Why the FourierTransform gives two different answers? > > In[1] FourierTransform[ (t - 5.0)^2*Exp[-(t - 5.0)^2 ], t, w] > > In[2] FourierTransform[ (t - 5)^2* Exp[-(t - 5)^2 ], t, w]