two integrals and a question about prime trinomials

[Karol PENSON]

       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
>


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Karol A. PENSON
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