Comment #5 on issue 2079 by ness...@googlemail.com: multiple integral gives
wrong result
http://code.google.com/p/sympy/issues/detail?id=2079
[I sent this by email while the tracker seemed to be down; sorry if it
comes up twice now.]
There are a couple of problems here, most of which are not really my fault:
- _eval_interval() can cause a NotImplementedError if certain limits cannot
be computed. Integral should be prepared to handle that; I'll fix this.
- series expansions of exponential integrals are not implemented - I will
fix this.
- limit() fails to call gruntz() - I will open an issue for this
If limit() is fixed, we will get through the first two integrals.
We can then compute a final antiderivative if we expand (polar or force) by
hand first, but this comes out somewhat nasty (because meijerint is used to
compute an antiderivative of log(z)/z and this is expressed as a G-function
on a set of measure zero).
Gruntz fails to do this final limit, both because of the piecewise and
because of the hypergeometric function involved. Doing some manual
tinkering (replacing the piecewise by the relevant part, removing the
hypergeometric function) the limit can be done and the integral evaluated
in terms of hypergeometric functions.
Making this work out of the box is going to be quite a bit of work; I
suggest leaving this issue open.
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