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Sep
5
awarded  Nice Answer
Jul
25
comment Result of Integrate depends on order of integration although the domain is rectangular
@Jens,@MichaelE2: According to The Lebesgue-Stieltjes integral, p. 118, absolute convergence implies that the order does not matter (Fubini's theorem). Nintegrate over the absolute integrand yields Numerical integration converging too slowly[...]. As I increase the upper limit, the integral seems to increase with always diminishing rate, which indicates that it converges. I'm not very knowledgeable about the intricacies of integration, as I'm a physicist. Apparently, I need to learn more...
Jul
25
asked Result of Integrate depends on order of integration although the domain is rectangular
Jul
24
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
It is correct, thanks. I get three results of varying complexity, depending on the version of Mathematica, and v. 10 cannot solve this if I swap the order of the variables of integration. v.10 after swap and yours give the simplest results. Unfortunately, the simplicity of the result does not remain constant or increase as the version increases, and it is quite obvious that most built-in simplifications do not work for the result I quoted above. Is there a way to configure how Integrate calculates the result?
Jul
23
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
Please disregard my previous comment. Mathematica 10 can find the integral if I change the order of integration. Mathematica 9 cannot find it in this case after waiting for tens of minutes.
Jul
23
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
Now this is getting weird: in v. 10 I get 1/2 Mass (1/r1 + \[Pi]/(2 Rotation) - ArcTan[r1/Rotation]/Rotation + ( Rotation ArcTan[Rotation/r1])/r1^2), which is the correct result and is much more simple than that of v.9, even though I didn't use Simplify and nothing, that I'm aware of, changed meanwhile!
Jul
23
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
@MitchellKaplan I didn't; @Öskå probably edited my question and replaced \[Theta] with $\theta$ etc.
Jul
23
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
Now that I tried it without Simplify, Mathematica 10 takes twice as long as Mathematica 9 albeit without result. The problem is not that Simplify is time-constrained; it is that the integral cannot be calculated.
Jul
23
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
I didn't, because it takes far longer in Mathematica 10 than in Mathematica 9 for this to return, which seems to be a bug, too.
Jul
23
asked Mathematica 10 fails to calculate integral that Mathematica 9 can handle
Jul
16
awarded  Scholar
Jul
16
accepted Infinite expression encountered when simplifying ArcTan sums although the result is finite
Jul
16
awarded  Commentator
Jul
16
comment Infinite expression encountered when simplifying ArcTan sums although the result is finite
Indeed, you have provided the answer to the original question, but I didn't know then that Mathematica's simplification functions are so sensitively dependent on the form of the expression. Thanks for your answer.
Jul
16
revised Infinite expression encountered when simplifying ArcTan sums although the result is finite
Append the full expression, because all methods of simplification fail with it
Jul
16
comment Infinite expression encountered when simplifying ArcTan sums although the result is finite
The infinite expression error persists even if I simplify this expression using the transformation in the answer here. I prefer that method, because it is more flexible and allows me to simplify, for example, the numerator of a fraction with ArcTan, on which Mathematica's facilities for simplification fail. Is there a way to prevent this error during a transformation?
Jul
15
comment Infinite expression encountered when simplifying ArcTan sums although the result is finite
@RahulNarain I tried the assumption x>0, still the same.
Jul
15
asked Infinite expression encountered when simplifying ArcTan sums although the result is finite
Jul
15
awarded  Editor
Jul
15
revised Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)
edited tags; edited title