The following integral occurs in computing the mean of the maximum
of three independent N(0,1) random variables:
I = sqrt(2/pi) \int_0^\infty u exp(-u^2) erf^3(u) du,
or, if you prefer maxima notation:
I = sqrt(2/%pi)*integrate(u*exp(-u^2)*(erf(u))^3,u,0,inf).
It appears that cos(pi^(3/2)*I) =10*sqrt(2)/27, though I cannot prove this.
Any suggestions?
Keith
Dr. Keith M. Briggs
Senior Mathematician, Complexity Research, BTexact Technologies
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