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

[Joel C. Salomon]

Andrei Alexandrescu wrote:
> 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!

These are sequences. (Or, in an EE context, “signals”, but let’s not go
there… ☺)

Except: a sequence might be the coefficients {α₀, α₁, α₂, …} of the
power _series_ α₀x⁰ + α₁x¹ + α₂x² + ⋯, in which case the sequence is
just a representation of the power series. There are some cool tricke to
be played with power series represented this way; e.g., see Doug
McIlroy’s “Squinting at Power Series” at
<http://plan9.bell-labs.com/who/rsc/thread/squint.pdf>.

—Joel Salomon