Andrei Alexandrescu wrote:
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!
I believe the mathematically correct terms would be RecursiveSequence
and ClosedFormSequence. If I were to use just Sequence, it would in fact
be for the latter.
A series is, as you said, the sum of all the terms in a sequence,
whereas summing only a finite set of terms gives a partial sum. (The
latter could be implemented as a range.)
A recurrence relation is an expression that recursively defines a
sequence (i.e. the string argument of the template).
I prefer MathWorld to Wikipedia when it comes to these things. Here are
some (possibly) useful links:
Recursive sequences:
http://mathworld.wolfram.com/RecursiveSequence.html
Some sequences that could possibly be rangeified:
http://mathworld.wolfram.com/Sequence.html
Series:
http://mathworld.wolfram.com/Series.html
Partial sums (and other sums) of sequences:
http://mathworld.wolfram.com/PartialSum.html
-Lars
