Re: More Integrate woes
- To: mathgroup at smc.vnet.net
- Subject: [mg9650] Re: More Integrate woes
- From: "Bill Bertram" <wkb at ansto.gov.au>
- Date: Mon, 17 Nov 1997 19:50:08 -0500
- Organization: Australian Nuclear Science and Technology Organisation
- Sender: owner-wri-mathgroup at wolfram.com
Colin Rose <NOHAMcrose at c2.telstra-mm.net.au> wrote in article
<64eaur$qn5 at smc.vnet.net>...
> In any statistical setting, calculation of the Gaussian distribution
> function is extremely important. Under Mathematica v3, this is
> something of a disaster.
>
>
> To summarise the problem:
>
> Under v3:
> ________
>
> Expressions such as:
>
> aa = Integrate[Exp[-x^2],{x,-Infinity,y},
> GenerateConditions->False]
>
> return output *of form*:
>
> 1 - Erf[Sqrt[y^2]]
>
> Our user now seeks numerical output. S/he enters:
>
> (aa /. y -> 3) == (aa/. y -> -3)
> True
>
> This is clearly FALSE.
Very strange!,
if you omit the "GenerateConditions->False" from the command, the output
from Mathematica 3 reads:
If[y < 0, -(1/2)*Sqrt[Pi]*(Erf[Sqrt[y^2]] - 1),
Integrate[Exp[-x^2], x, -Infinity, y]]
which implies that the Erf solution is only valid for negative y, and
now
(aa /. y -> 3) == (aa/. y -> -3)
returns False.
However, for positive y Mathematica 3 does not seem to be able to
perform the integration!
This may well be classified as a bug in this version of Mathematica.
Cheers,
Bill Bertram
ANSTO