> e := sinh(log(sinh(-log(z)/2))); > f := simplify(e): > series(e-f,x); produces a series with sqrt(z) as leading coefficients. Numerically (and via simplify@evalc), e-f is 0.

Everything is supposed to be homogeneous, so you have to interpret that '1' as the identity operator. They are saying that x*Dx-I as a differential operation (I=identity op, Dx = d/dx) annihilates x.

Everything is supposed to be homogeneous, so you have to interpret that '1' as the identity operator. They are saying that x*Dx-I as a differential operation (I=identity op, Dx = d/dx) annihilates x.

The Mathematics of Gambling, by Edward Thorp.

h(x,a) means an arbitrary function of x and a. x is just a variable. sys1 is correct, it says that the function h(x,a)=x (ie the identity function in the first variable) satifies the PDE sys1. It is too bad that this worksheet is so dated, because the material it contains really is quite beautiful. Though most of it (with a few minor adjustments) should still work in Maple 11.

h(x,a) means an arbitrary function of x and a. x is just a variable. sys1 is correct, it says that the function h(x,a)=x (ie the identity function in the first variable) satifies the PDE sys1. It is too bad that this worksheet is so dated, because the material it contains really is quite beautiful. Though most of it (with a few minor adjustments) should still work in Maple 11.

I would recommend you use a combination of Maple (and the packages 'gfun', 'DEtools'), probably download MGFun from the same INRIA site, and asking questions on mapleprimes. Especially in view of what you're trying to do (I'll respond to that seperately).

I would recommend you use a combination of Maple (and the packages 'gfun', 'DEtools'), probably download MGFun from the same INRIA site, and asking questions on mapleprimes. Especially in view of what you're trying to do (I'll respond to that seperately).

Much to many people's chagrin (here on primes, and others I am sure), Maplesoft has made it abundantly clear that bugs in Classic will not be fixed. If you can reproduce it on Standard, then you might get some traction (to have it fixed in Standard). Reporting bugs in person tends to be useless - it needs to be in the database for it to have a better chance of getting fixed. And my confidence that all bugs reported in this forum actually make it to the database is low. support@maplesoft.com does seem to be the 'best bet' to ensure that the bug gets properly filed. Of course, the Maplesoft minders of www.mapleprimes.com could reassure us that every single bug listed on here gets filed [probably by posting the unique identifier for each bug filed from here]. That would be nice indeed.

And Kelly Roach improved on that for Maple.

And Kelly Roach improved on that for Maple.

Maple contains what I thought to be a complete implementation of integration via G-functions (especially of the kind that started this thread). So I must admit that I was really surprised that Maple could not simply "compute" this integral. To me, it feels like a bug (rather than a simple weakness) that it returns unevaluated in Maple.

Maple contains what I thought to be a complete implementation of integration via G-functions (especially of the kind that started this thread). So I must admit that I was really surprised that Maple could not simply "compute" this integral. To me, it feels like a bug (rather than a simple weakness) that it returns unevaluated in Maple.

It is possible that this is "just a bug". It might be that Maplesoft did not have enough real 'use cases' from real users to test their Toolbox against, and so made some mistakes. You should make sure to also email your bug reports to support@maplesoft.com. And do continue to report such things prominently -- embarassing bugs have this way of getting fixed faster...

The job of a teacher is to teach students the 'right' way to do things. Then, we also teach them to deal with situations where things are done in chaotic, haphazard ways. It seems that you view employees as automatons: obey or else. In the so-called "knowledge industry", that is a good way to have all your good employees quit on you. I used to be in industry, and I have seen bad bosses (who dictate to employees what needs to be done, even when the boss is quite clearly wrong). Result: all the good programmers left, and for the rest, morale was very low. The boss eventually gets turfed too, because of his combined incompetence and the fact that his team is now devoid of talent. My best employees (then), and my best grad students (now) are the ones who tell me right away when I am wrong, and can prove it. That is the only way I know of keeping intelligent and creative individuals productive and happy. And I like it, because it keeps me on my toes. About mathematically correct answers: one of the reasons that Maple does not always return the right answer is that doing so might take too much time, or cripple the overall power too much [or at least, that's the party line]. Axiom and Derive are two examples of computer algebra software more reliable than Maple, and neither survived contact with the marketplace. On the other hand, I have long fought on the side of 'correctness', even if that means losing some efficiency.