Re: Hilbert transform bug in 7.0.3?

*To*: mathgroup at smc.vnet.net*Subject*: [mg100930] Re: Hilbert transform bug in 7.0.3?*From*: Nacho <ncc1701zzz at gmail.com>*Date*: Thu, 18 Jun 2009 06:17:54 -0400 (EDT)*References*: <h19i5r$p4g$1@smc.vnet.net> <h1a9pf$7vv$1@smc.vnet.net>

Hi Daniel. You are right, without PrincipalValues, it works fine. I took the definition from Mathworld directly, and it seems it works with the PrincipalValues->True in previous versions. Thanks. Regards. On Jun 17, 10:33 am, dh <d... at metrohm.com> wrote: > Hi Nacho, > > your problem comes from the fact that you are using PrincipalValue -> > > True together with DiracDelta. Consider the simplest case: > > Integrate[DiracDelta[x], {x, -Infinity, Infinity}] > > Integrate[DiracDelta[x], {x, -Infinity, Infinity},PrincipalValue -> True] > > The first integral gives 1 in agreement with the definition of > > DiracDelta. The second integral is actually a limit of two integrals. > > One from -Infinity to epsilon. The second from epsilon to Infinity. For > > epsilon > 0 both integrals are zero. Therefore, the limit is also zero. > > Daniel >