see inline. On Fri, Jun 29, 2012 at 5:04 AM, Vinzent Steinberg <vinzent.steinb...@gmail.com> wrote: > Am Montag, 25. Juni 2012 21:14:38 UTC+2 schrieb kjetil1001: >> >> > Actually you can work around this limitation by using piecewise >> > functions: >> > >> > In [12]: myabs = lambda x: Piecewise((x, x>=0), (-x, x<0)) >> > >> > In [13]: integrate( (t1*t2*t3)**beta * myabs((t1-t2)*(t1-t3)*(t2-t3)), >> > (t1,0,1),(t2,0,1),(t3,0,1)).doit() >> > Out[13]: 0 >> >> But that answer 0 is wrong! > > > You are right, it should not be 0, this is a bug. Do you know the correct > value? >
Yes. This is a special case of the so-called Selberg integral (named for Atle Selberg) , see http://en.wikipedia.org/wiki/Selberg_integral The special case above has the value: (G is the gamma function) S_3(beta+1,1,gamma=1/2) = \prod_{j=1}^3 \frac{ G(beta+1+(j-1)gamma) G(1+(j-1)gamma) G(1+j gamma) } { G(beta+2+(3+j-2)gamma) G(1+gamma) } Kjetil > Vinzent > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To view this discussion on the web visit > https://groups.google.com/d/msg/sympy/-/V4hsllBr76sJ. > > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. -- "If you want a picture of the future - imagine a boot stamping on the human face - forever." George Orwell (1984) -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
