On Wed, Feb 4, 2009 at 8:26 AM, Andrei Alexandrescu <[email protected]> wrote: > 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!
My digital signal processing textbook refers to "discrete-time sequences", not series. But I'm pretty sure I've heard "discrete-time series" used too. So I'd say either sequence or series is just fine. But that's just the EE perspective. Pure math guys might have a different take. --bb
