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
phone: +44(0)1473 work: 641 911 home: 610 517 fax: 642 161
profile: http://www.btexact.com/ideas/profiles?doc=42493
web: http://more.btexact.com/people/briggsk2/
mail: Keith Briggs, Polaris 134, Adastral Park, Martlesham, Suffolk
IP5 3RE, UK
|