[seqfan] Re: need algebra proof

[Richard Mathar]

On http://list.seqfan.eu/pipermail/seqfan/2010-March/004072.html

we had earlier correspondences, which -- it's 11:30 pm and I'm getting lazy --
are copied-n-pasted for your pleasure

rjm> From: Richard Mathar <mathar at strw.leidenuniv.nl>
rjm> Date: Tue, 09 Feb 2010 23:29:30 +0100
rjm> Organization: Leiden Observatory, The Netherlands
rjm> To: qntmpkt at hotmail.com
rjm> Subject: Re: new transform - Gary
rjm> Cc: maximilian.hasler at gmail.com, mathar at strw.leidenuniv.nl
rjm> ..
rjm> 
rjm> IN generatign function terms, you are searching the solution
rjm> to S(x)=A(x)/A(x^2), where A(x) is the unknown. The example
rjm> of starting with S(x) = sum_i i*x^(i-1), a shifted version of A000027,
rjm> gives A(x) in A171238. The standard physicist's way of finding A(x)
rjm> is to start with A(x) = S(x) as an ansatz, and then
rjm> to iterate  A(X)  := S(x)*A(x^2) repeatedly. I think this
rjm> is called a B"urmann-Lagrange series...what Kepler did as you know,
rjm> but no correct mathematician would ever accept. Paul Barry seems to
rjm> provide a lot of sequences defined through this type of explicit
rjm> requirement on A(x^2) as a function of A(x). You may ask him what
rjm> the history of this is..