two integrals and a question about prime trinomials
Alec Mihailovs
alec at mihailovs.com
Fri Feb 25 21:28:31 CET 2005
----- Original Message -----
From: "Karol PENSON" <penson at lptl.jussieu.fr>
> 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 ?
I used Maple 10. It can do this more general integral, too,
int( exp(-p*x^2)*erf(a*x)*erf(b*x), x=0..infinity) assuming p>0;
a b
arctan(---------------------)
2 2 1/2 1/2
(a + b + p) p
-----------------------------
1/2
(Pi p)
Alec Mihailovs
http://math.tntech.edu/alec/
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