ch-ch-update: series, closed-form series, and strides

[Andrei Alexandrescu]

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