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6h
reviewed Close Simplify expression by restricting variable to be integer
16h
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
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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.
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awarded  Nice Answer
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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.
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reviewed Close Why isn't Refresh working as expected?
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awarded  Nice Answer
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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).
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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.
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revised Symbolic solution(s) to generalized Heat equation
Added check
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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).
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revised Symbolic solution(s) to generalized Heat equation
Green function added
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answered Symbolic solution(s) to generalized Heat equation
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comment HoldForm doesn't hold form
Great analysis and solution for the main issue - it also works for FrameLabel where the same issue appeared.
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accepted HoldForm doesn't hold form
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awarded  Nice Question
Jul
22
revised HoldForm doesn't hold form
Version info updated
Jul
22
comment HoldForm doesn't hold form
What you observed also holds for Hold in the same context, so you must have hit the nail on the head. I think this cannot have been done intentionally - it makes no sense.
Jul
22
comment HoldForm doesn't hold form
I suspected that one could find a working character encoding, but of course I would like to keep the default encoding. Anyway, thanks for that find, too! In terms of using Inactive[Set], I would then probably not bother and rewrite everything with FormBoxes. But the fact that Hold has the same issue as HoldForm in AxesLabel really worries me.
Jul
22
comment HoldForm doesn't hold form
That's a valuable observation, thanks!