Re: A beginer's simple question about Mathematica...
- To: mathgroup at smc.vnet.net
- Subject: [mg63548] Re: A beginer's simple question about Mathematica...
- From: dh <dh at metrohm.ch>
- Date: Thu, 5 Jan 2006 03:12:16 -0500 (EST)
- References: <dpg11e$pm4$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
it looks as you fooled yourself. In the output there is a variable p
that does not appear in the input.
Apart from this, you got something of the form:
fac * If[condition, result1, result2]
only that Mathematica did write it, for some unknown reason, a bit more
complicated.
The condition is:
Re[z] > -1/2 && Re[(b + c + 4*a*z^2)/(8*a*b + 8*a*c)] > 0
result1 is a pretty complicated expression
result2 contains a further integral Mathematica was unable to do
and fac is:
(Sqrt[2]*Sqrt[p])/Sqrt[b^(-1) + c^(-1)]
Daniel
leelsuc at yahoo.com wrote:
> I try to run
>
> Integrate[x*Exp[-((x-2*a)^2/(8*a)+(y-b)^2/(2*b)+(z*x-y-c)^2/(2*c))],{x,-\[infinity],0},{y,-\[infinity],+\[infinity]}]
>
> get
>
> \!\(\(\(1\/\@\(1\/b +
> 1\/c\)\)\((\@\(2\ p\)\ If[Re[z] > \(-\(1\/2\)\) && Re[\(b + c +
> 4\ a\ z\
> \^2\)\/\(8\ a\ b +
> 8\ a\ c\)] >
> 0, \(-\(\(2\ \[ExponentialE]\^\(1\/2\ \((\(-a\) - b -
> \
> c)\)\)\ \((\(-\[ExponentialE]\^\(\(a\ \((b + c)\)\ \((1 + 2\
> z)\)\^2\)\/\(2\ \
> \((b + c + 4\
> a\ z\^2)\)\)\)\)\ \@\(2\ p\)\ \((1 + 2\ z)\) + 2\
> \@\(\(b + c \
> + 4\ a\ z\^2\)\/\(a\ b + a\ c\)\) + \[ExponentialE]\^\(\(a\ \((b +
> c)\)\ \((1 \
> + 2\ z)\)\^2\)\/\(2\ \((b + c + 4\ a\ z\^2)\)\)\)\ \@\(2\ p\)\ \((1 +
> 2\ z)\)\
> \ Erf[\(1 + 2\ z\)\/\(\@2\ \@\(\(b + c + 4\ a\ z\^2\)\/\(a\ b + a\ \
> c\)\)\)])\)\)\/\((\(b + c + 4\ a\ z\^2\)\/\(a\ b + a\
> c\))\)\^\(3/2\)\)\),
> Integrate[\(-\[ExponentialE]\^\(-\(\(4\ a\^2\ \((b
> + c)\) \
> + \((b + c)\)\ x\^2 + 4\ a\ \((b\^2 + c\^2 +
> x\^2\ z\^2 - c\ \((\(-x\) - 2\ x\ z)\) + b\ \((2\ c
> + x\ \
> \((1 + 2\ z)\))\))\)\)\/\(8\ a\ \((b + c)\)\)\)\)\)\ x, {x, 0, 8}, \
> Assumptions -> Re[z] = \(-\(1\/2\)\) || \((Re[z] > \(-\(1\/2\)\) &&
> Re[\(b + \
> c + 4\ a\ z\^2\)\/\(8\ a\ b + 8\ a\ c\)] = 0)\)]])\)\)\)
>
>
> What does this result mean?
>
> Thanks a lot for replying.
>