Joel C. Salomon wrote:
Steven Schveighoffer wrote:
I don't think such a series is definable with Andrei's template. I think
his series template is only usable in situations where computing a[n]
depends only on n and the elements a[n-X]..a[n-1], where X is a constant.
I'm not really a mathemetician, so I don't know the technical term for the
differences, I'm sure there is one.
Time-invariant, or shift-invariant.
Great! I didn't know (haven't learned college-level Math in English;
sometimes I wonder how I fumbled through grad school without major
misunderstandings). By the way, I might have been wrong with the name
"series" itself. I thought "series" is something like a_n =
f(a_{n-1},...,f_a{n-k}). However, according to Wikipedia:
http://en.wikipedia.org/wiki/Infinite_series
series is really what I thought is called "partial sums", i.e. s_n is
the sum of elements of a sequence a_n up to the nth element.
So should I change "series" with "sequence"? How about what I called
"ClosedFormSeries"? By that I meant a series, (pardon, sequence), in
which there is no recurrence formula - the nth element a_n can be
expressed in terms of n and a[0], ..., a[k] (a sort of "random access"
for a sequence).
So, what names should I use? English-speaking mathematicians across the
newsgroup, unite!
Andrei
