two integrals and a question about prime trinomials
Karol PENSON
penson at lptl.jussieu.fr
Fri Feb 25 19:57:35 CET 2005
The integral , in Maple notation, int(
exp(-2*x^2)*(erf(x))^2,x=0..infinity) is a special case of a
more general integral :
int( exp(-p*x^2)*erf(b*x)*erf(c*x), x=0..infinity) =
(1/sqrt(Pi*p))*arctan(b*c/sqrt(p*(b^2+c^2+p)),
see: A.P.Prudnikov, Yu.A.Brychkov and O.I.Marichev , Integrals
and Series, vol.2 - Special Functions,
(Gordon & Breach, 1998) , integral no. 2.8.19.8 , p.123, where
also restrictions on p, b and c
can be found.
Alec, I have tried this integral with Maple 9 and obtained nothing.
Which version of Maple do you use ?
Karol A. Penson
Alec Mihailovs
wrote:
> ----- Original Message ----- From: "Eric W. Weisstein" <eww at wolfram.com>
>
>>
>> Integrate[Exp[-2x^2]Erf[x]^2,{x,0,Infinity}]
>
>
> This one can be done in Maple,
>
>> int(exp(-2*x^2)*erf(x)^2,x=0..infinity);
>
>
> 1/2
> 1/2 2
> 2 arctan(----)
> 4
> 1/2 -----------------
> 1/2
> Pi
> Alec
>
--
_________________________________________________________________________
Karol A. PENSON
Universite Paris 6 | Internet : penson at lptl.jussieu.fr.
Lab. Physique Theorique des |
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