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Aug 30, 2010 at 4:13 comment added fedja Ok. Then it would be interesting to know what are the properties you want whose proof currently gives you trouble. I mean, this may result in a more productive search of a "good representation" than the blind symbolic manipulation and guesswork we are restricted to now.
Aug 30, 2010 at 2:58 comment added John D. Cook Thanks. Ultimately I'm not as interested in a close-form expression as I am various properties of the function you call J. But if there's a convenient expression for J, I'd take advantage of it. Your differential equation might lead to an interesting approach. I'll look into that. The function erfc isn't elementary, but it's well-known: you can look up approximations, asymptotic series, etc. So you could say I'm looking for an integral in "famous" terms rather than "elementary" terms.
Aug 30, 2010 at 2:49 history answered fedja CC BY-SA 2.5