Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Integration WrongResult
New issue 3317 by [email protected]: failing integral with abs()
http://code.google.com/p/sympy/issues/detail?id=3317
In [1]: var('t1:4')
Out[1]: (t₁, t₂, t₃)
In [2]: var('beta')
Out[2]: β
In [3]: integrate( (t1*t2*t3)**beta * abs((t1-t2)*(t1-t3)*(t2-t3)),
[hangs...]
In [4]: myabs = lambda x: Piecewise((x, x>=0), (-x, x<0))
In [5]: integrate( (t1*t2*t3)**beta *
myabs((t1-t2)*(t1-t3)*(t2-t3)),(t1,0,1),(t2,0,1),(t3,0,1))
Out[5]: 0
This is incorrect, the expected answer is:
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) }
where G is the gamma function. (See [1].)
Thanks to Kjetil for pointing this out, see [2] for the discussion.
[1] http://en.wikipedia.org/wiki/Selberg_integral
[2] https://groups.google.com/forum/?fromgroups#!topic/sympy/-Pv-jLTkfes
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