[seqfan] Re: "Expansion of ..." versus "G.f. = ..."

[Neil Sloane]

PS  I really don't want to be on the opposite side of the fence from some
of the top editors.

How about a compromise: I will change those definitions to something with
this format:

Generating function Sum_{k >= 0} a(n)*x^n = Sum_{k>=1}
x^(k*(3*k+1)/2)/(1-x^k).

That makes it clear even if you are not certain what g.f. stands for, and
if you do know, it makes it explicit.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Thu, Dec 3, 2020 at 9:00 PM Neil Sloane <njasloane at gmail.com> wrote:

> Dear Sequence Fans,  In the OEIS "g.f." has a precise technical meaning:
> it means the ordinary generating function Sum_n a(n)*x^n.
>
> On the other hand, to describe a sequence as the "expansion of [some
> function]" is not precise at all.
>
> You could say that 1,2,4,8,16,32,64,... arises from the expansion of
> 1+2x^2+4x^4+8x^6+16x^8+32x^10+64x^12+ ..., and it would be correct and true.
>
> So when I define a sequence by saying it has g.f. = [something], that is a
> more precise statement than saying it arises from the expansion of
> [something] .
>
> I am writing this because I have noticed that my definitions of sequences
> sometimes get changed - for the worse - without anyone telling me.
>
> I guess that the reason for making this "improvement" is so that we don't
> scare people. Well, I think that they are more likely to be scared by the
> idea of an expanding formula: imagine
>
>    Sum_{k>=1} x^k/(1-x^k)
>
> getting bigger and bigger and BIGGER until it fills the tiny little screen
> on their phone!
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>