Hey
I'm not a Haskell (or any other functional language) programmer, so I don't know what all these mean. But I'll take a stab (newb warning, advice may be wrong)
> The ordered sequence of [1,2,3...].
lo porsi be tu'a lo banro bei lo'i rarna'u
vo'i lo'i rarna'u
> The ordered sequence which results from doubling every term in the above. i.e. map (*2) [1..]
li 2 pi'i py
For appropriately overloaded pi'i, and assuming the about sequence is py.
> The sets corresponding to the sequences above.The first 10 terms of the sequence [1,2...].
lu'i py - use lu'i to turn things into sets
Not sure how to make ranged selection
> The sequence [1,2...10].
> The sequence [1,3,5...9].
li 1 ce'o 3 ce'o 5 ce'o 7 ce'o 9
I don't know a way to express ellipsis
> The sum of the above sequence.
li si'i sy
> The product of the sequence 2 above.
I don't know; there is no product equivelent to sigma notation in VUhU. Maybe:
li na'u poipi'i te'u sy
> f(x,y) = (x+y)*y. (I'm fairly certain I know where to look for this in CLL, but I'm including it for completeness)
me'o ma'o fy boi xy boi y'y fancu fo me'o pi'i su'i xy boi y'y ku'e y'y
> foldl f [1..4]. (with f as defined above)
Don't know what this means.
> [x^2 | x <- [1..]]. (the list comprehension)
> {x^2 | x is an element of the natural numbers}. (the set comprehension)
lo'i pilji be ny bei ny
Not sure how to correctly restrict ny to the naturals.
It would be awesome if lojban mex had a (reasonably developed) type system, and the operators overloaded appropriately. I believe minimiscience was working on such a system, judging from their work on the bpfk mex operators page (http://www.lojban.org/tiki/tiki-index.php?page=BPFK+Section%3A+MEX+Operators). I've messed around with some ideas, but not developed anything substantial (got sidetracked with a lojban parser project).
As for resources. The most significant work on maths in lojban that I know of is a translation of the first chapter of a book about (higher) algebra. It's on the page Robin linked. I started a translation of a chapter of Evans and Gariepy, which I'm going to try and finish today. I think there are a few pages coining some terminology (http://www.lojban.org/tiki/Math+terminology), but imo it is fairly minimal.
At the moment, I would agree with Robin that mekso is unsuitable for anything more than simple things. I tend to use a more hybrid approach though.
mu'o mi'e ros