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1h
comment Result of Integrate depends on order of integration although the domain is rectangular
@MichaelE2 I agree, and I think version 10 should recognize the divergence more quickly, as is the case in version 8 (and apparently in 9). Maybe it gets stuck in trying to combine some ConditionalExpressions. Don't have time to investigate right now...
3h
comment Result of Integrate depends on order of integration although the domain is rectangular
The fact that integration order matters in this case seems to be due to the fact that the integration in r goes to infinity, so the domain isn't compact. However, I do agree that the behavior of Mathematica has changed, and it would be good to understand better why that is.
3h
revised Result of Integrate depends on order of integration although the domain is rectangular
Corrected a typo
9h
awarded  Nice Answer
18h
reviewed Close Simplify expression by restricting variable to be integer
1d
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
@MitchellKaplan Here is a nice tool you can install in order to format your code with Greek letters etc.: Additional useful buttons for our M.SE editor
2d
comment Symbolic solution(s) to generalized Heat equation
Do your comments always run this long? Just kidding. In the Heat function, you should add Assumptions->t>0 to the Integrate to speed it up and avoid ConditionalExpression in the output.
2d
awarded  Nice Answer
2d
comment Symbolic solution(s) to generalized Heat equation
I would rather not try to broaden the question so much. It's basically a task for a curator to gather the existing Green's functions for various problems. Fully automating this would require a lot of effort: recognizing the type of equation, bringing it to some standard form etc. This would not fit into the format of a Q&A site like this, I think.
2d
reviewed Close Why isn't Refresh working as expected?
Jul
22
awarded  Nice Answer
Jul
22
comment Symbolic solution(s) to generalized Heat equation
@chris Yes, that's true, it's a trick that works for the heat equation and also the Schrödinger equation. I omitted a bunch of steps that would be needed to get there from the spectral integral as one usually finds it in textbooks. The general relation for the Green's function in terms of eigenfunctions is however also something that could be automated. Only enforcing the convergence of the integral may in general be a problem. That's where specific tricks come in handy. What I showed is the shortest possible calculation I know of, for this case (i.e., the heat eq. in the question).
Jul
22
comment Symbolic solution(s) to generalized Heat equation
Not sure either, but I up-voted yours to cancel the downvote. Anyway, as your answer shows there is potential for generalizations. But I did say that already, too... so really this isn't a separate answer to the original question. It's more a comment.
Jul
22
revised Symbolic solution(s) to generalized Heat equation
Added check
Jul
22
comment Symbolic solution(s) to generalized Heat equation
@chris Upping the dimensions is one possibility, and automating the Green's function is another. Both can be automated to some extent - which is to say that there is definitely room for Wolfram to add some functionality. But yes, it should be possible for us to do some of their work for them... with the caveat that it will probably break in less standard cases (e.g., elliptical coordinates are already much harder).
Jul
22
revised Symbolic solution(s) to generalized Heat equation
Green function added
Jul
22
answered Symbolic solution(s) to generalized Heat equation
Jul
22
comment HoldForm doesn't hold form
Great analysis and solution for the main issue - it also works for FrameLabel where the same issue appeared.
Jul
22
accepted HoldForm doesn't hold form
Jul
22
awarded  Nice Question