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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
>
> 




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