On Thu December 22 2005 05:54, M. Edward (Ed) Borasky wrote: > There are unanswered questions about the hydrogen atom in 2005? :) > > Seriously, though, have you thrown this at Derive? An HP or TI handheld? > Those pesky "student grade" tools sometimes surprise people. I've > actually got all three, so I could do it if you haven't. Have you tried > Reduce? I didn't really expect this to work but I tried anyway on a HP 28C. But as the manual says " It can return an exact inegral (indefinite) of an expression that is a polynomial in the variable of integration. Otherwise it can give an approximation based on the Taylor series. But when I tried it, I just got "out of memory" (Degree of polynomial set to 3)
Richard harke > > Bob McElrath wrote: > >I don't know whether to file this as a bug or not, since it seems the > >solution to this integral is not known. (None of Maple, Mathematica, > >Maxima can do it, and in addition it does not seem to be in G&R) > > > >So, any integral experts want to take a crack at it? In the problem I > >am interested in, a is real and a>0, b is real and 0 <= b <= 1, and I > >need the integral over theta=0..2*Pi, in case the definite integral is > >easier. > > > >(3) -> integrate(exp(-a*sqrt(1-b*cos(theta))), theta) > > 3) -> > > > > >> Error detected within library code: > > > > Function not supported by Risch d.e. > > > >This has arisen in a quantum mechanical calculation involving the > >Hydrogen atom. > > > >Since the integrand is well-behaved, I have chosen to do this > >numerically for my paper, however an analytic solution would be > >desirable. I'm having to carry out a 3-dimensional numeric integral > >using the Cuhre method because the above integral is not known, and the > >second of the three integrals is over things inside 'b' above, and is in > >general quite complicated. The third is even more nasty, and I think > >I'd have to do numerically anyway. > > > >But, I'm surprised to find that such a simple integral has no known > >solution. > > > >-- > >Cheers, > >Bob McElrath [Univ. of California at Davis, Department of Physics] > > > > "In science, 'fact' can only mean 'confirmed to such a degree that it > > would be perverse to withhold provisional assent.' I suppose that > > apples might start to rise tomorrow, but the possibility does not > > merit equal time in physics classrooms." -- Stephen Jay Gould (1941 - > > 2002) > > > > > >------------------------------------------------------------------------ > > > >_______________________________________________ > >Axiom-developer mailing list > >Axiom-developer@nongnu.org > >http://lists.nongnu.org/mailman/listinfo/axiom-developer _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
