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

[Bill Baxter]

On Wed, Feb 4, 2009 at 8:26 AM, Andrei Alexandrescu
<SeeWebsiteForEmail at erdani.org> 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