Re: Multiple integration: bug?
- To: mathgroup at smc.vnet.net
- Subject: [mg122483] Re: Multiple integration: bug?
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Sat, 29 Oct 2011 07:14:50 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <j89vct$224$1@smc.vnet.net>
Thank you all for the valuable hints. --- Wolfgang "Dr. Wolfgang Hintze" <weh at snafu.de> schrieb im Newsbeitrag news:j89vct$224$1 at smc.vnet.net... > In calculating Integrals of the type Integrate[0<x1<x2<...<xn<1] > which > should give 1/n! I observed a strange behaviour > > Using UnitStep[] it works fine for n=2 to n=5: > > In[48]:= > Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] - > x[3]]*UnitStep[x[5] - x[4]], {x[1], 0, 1}, {x[2], 0, 1}, {x[3], 0, > 1}, > {x[4], 0, 1}, {x[5], 0, 1}] > Out[48]= > 1/120 > > > It gives nonsense for n=6 (and higher): > > In[47]:= > Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] - > x[3]]*UnitStep[x[5] - x[4]]*UnitStep[x[6] - x[5]], {x[1], 0, 1}, > {x[2], > 0, 1}, {x[3], 0, 1}, {x[4], 0, 1}, {x[5], 0, 1}, > {x[6], 0, 1}] > Out[47]= > -(1/4) > > Is this a bug or did I make a mistake somewhere (did not consider > bounds or depth level etc.)? > > Any comment is appreciated. > > BTW: using Boolean instead of UnitStep seems to have no restriction. > > --- Wolfgang > >