May. 8th, 2007

synchcola: (heyoka "ok")
I went to the library and read van Peype's paper, sort of (it's still in German).

I have a question. Watson says that that integral I3, or let's say I3(0) where
I_3({\bf p}) = {1 \over 8\pi^3} \int_0^{2\pi} \int_0^{2\pi} \int_0^{2\pi} {e^{i(\theta_1 p_1 + \theta_2 p_2 + \theta_3 p_3)} \over 3 - \cos\theta_1 - \cos\theta_2 - \cos\theta_3} \,d\theta_1 \,d\theta_2 \,d\theta_3,
appeared in the paper by van Peype. But it seemed as though the integrals I3(0, 0, 1) and I3(0, 1, 1) were more important. Can those integrals also be evaluated? *boggle* Oh wait, the answer is yes? But was it really only proved in 2002? *double boggle*

Also in that paper they totally said thatand after prodigious efforts, ancient astronauts have   alien technology   actual scientists have   mathematicians have found a closed form for the above integral. (J0 is used to mean the zeroth Bessel function.)

What if there's a closed form for $\mathfrak{L}\big[J_0(it)^4\big]$? What then?

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