The performance characteristics of the user interface and the kernel (ie the math) are very different on different machines/OS combinations.  But generally speaking the math is usually quite good and fast, but on some platforms the (Standard) interface can be rather sluggish.  And on a Mac, you have no choice, Standard is all there is. 

You wanted to know if that sum behaves asymptotically as O(1/x) for x large -- which is exactly what the asymptotic series above shows.  Even better, you get the actual constant as well as the next few terms in the expansion.

You wanted to know if that sum behaves asymptotically as O(1/x) for x large -- which is exactly what the asymptotic series above shows.  Even better, you get the actual constant as well as the next few terms in the expansion.

It means convex but only on paths which are aligned with an axis rather than between arbitrary points, ie on straight lines parallel to an axis.

I have no idea if there is standard terminology for this -- there might not be.  I just 'invented' "axis convex" as it seemed like the obvious description of what I had in mind.

> f:= sum(1/n^2,n=x+1..infinity): asympt(f,x);

                        1      1       1        1
                 1/x - ---- + ---- - ----- + O(----)
                          2      3       5       6
                       2 x    6 x    30 x       x

You can get as many terms in this asymptotic expansion as you want.

> f:= sum(1/n^2,n=x+1..infinity): asympt(f,x);

                        1      1       1        1
                 1/x - ---- + ---- - ----- + O(----)
                          2      3       5       6
                       2 x    6 x    30 x       x

You can get as many terms in this asymptotic expansion as you want.

AFAIK it has been reported before too.  It affects a lot of other help pages as well.  It might be fixed in Maple 12 though, that would be nice.

I believe that that is the function you want.  The GUI's parser is written in Maple code [since that is a 1000 times easier than in most other languages].

There is no way to prevent automatic simplifications from the kernel if you are going to involve native Maple objects.  For example 2+5 will always transform to 7 at the top-level (and other times too).  Anytime the DAG (represented by) _Inert_SUM(_Inert_POSINT(2),_Inert_POSINT(5)) is encountered, basically any manipulation of it by Maple will transform it to 7.  Only if you manipulate it abstractly (i.e. using alternate data-structures) can you prevent automatic simplifications.

In other words, anytime you transform some external syntax in 'Maple', automatic simplifications kick in. 

I believe that that is the function you want.  The GUI's parser is written in Maple code [since that is a 1000 times easier than in most other languages].

There is no way to prevent automatic simplifications from the kernel if you are going to involve native Maple objects.  For example 2+5 will always transform to 7 at the top-level (and other times too).  Anytime the DAG (represented by) _Inert_SUM(_Inert_POSINT(2),_Inert_POSINT(5)) is encountered, basically any manipulation of it by Maple will transform it to 7.  Only if you manipulate it abstractly (i.e. using alternate data-structures) can you prevent automatic simplifications.

In other words, anytime you transform some external syntax in 'Maple', automatic simplifications kick in. 

You are quite right.  But for a quadrilateral which starts axis-aligned into a general one, the formulas for adjusting the bounds to 'respect' (u,v) axes are not too bad.  And this is one of the formulas that really needs figured out.

In a slightly more general case, geometry really kicks in: what if the shape you are integrating over is axis-convex in its original formulation [essentially true by definition], but no longer so after a change of variables?  There is then no real way to express the new integral in these new coordinates!  However, for convex shapes, it should always work.  But isn't that interesting though, that out of seemingly nowhere convexity shows up as a crucial condition?  I certainly did not expect that a priori, but only after working on this problem for a while; of course now it seems obvious!

Matlab allows this.

Now, that is really interesting!  Could you perhaps start a new thread (blog post?) where you give us links to Matlab's documentation of this feature?

Matlab allows this.

Now, that is really interesting!  Could you perhaps start a new thread (blog post?) where you give us links to Matlab's documentation of this feature?

Maple makes it quite easy to add new 'math' functions like this, so if you think this is needed, add it.

Now, if what you are asking is for Maplesoft to start doing lots of research to start using this function in 'int' and 'dsolve' (and so also in simplify, etc), well, that's likely to take years.  If you were to show (by building a prototype and publishing a paper or two about it) that this is really really useful, then I think there would be more interest.

Otherwise the problem is that there are all sorts of other functions still to be done (the FoxH function and the bivariate Lauricella functions probably being next).

Congratulations on getting 1000 points Robert. 

Congratulations on getting 1000 points Robert.