Bill Gosper <billgosper@gmail.com> wrote:

J?rg>Nice.

...

Could you supply an non-garbled version (image?) of the things below (c45)? Here's a png <http://gosper.org/r-r2x2.png>. I haven't yet figured out how to get the sums = products from the 3x3s.

Interestingly, an eavesdropper also got a garble, but it was ungarbled (except for nonfixed font) as quoted back to me. Sometimes you can just delete some spurious linebreaks. But isn't it high time math-fun supported typesetting? I resorted to Macsyma's ancient ASCII rendering due to OutputForm's industrial strength preemptive garbling. --rwg

J?rg>These may be of interest:

{Johann Cigler: {A new class of $q$-Fibonacci polynomials}, The Electronic Journal of Combinatorics, vol.10, no.1, (2003). URL: \url{http://www.combinatorics.org/Volume_10/Abstracts/v10i1r19.html}.}

{Johann Cigler: {$q$-Fibonacci Polynomials and the Rogers-Ramanujan Identities}, Annals of Combinatorics, vol.8, no.3, pp.269-285, (September-2004). URL: \url{http://homepage.univie.ac.at/johann.cigler/preprints/fibon.pdf}.}

(I can email the final version of second, it's pay-walled).

Possibly more pertinent papers at http://homepage.univie.ac.at/johann.cigler/electr.html

Regards, jj

* Bill Gosper <billgosper@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> [Oct 08. 2012 08:02]:> (For R-R, special-case a:=q)> > (c44) 'PRODUCT(MATRIX([0,A],[Q^K,1]),K,0,INF) => MATRIX([0,SUM(A^(N+1)*Q^N^2/QPOCH(Q,Q,N),N,0,INF)],[0,SUM(A^N*Q^(N^2-N)/QPOCH(Q,Q,N),N,0,INF)]);>

...

[ inf 2 ]>

[ ==== n n ]> [ \ a q ]> [ 0 a > -------------- ]> inf [ / qpoch(q, q, n) ]> /===\ [ ==== ]> | | [ 0 a ] [ n = 0 ]> (d44) | | [ ] = [ ]> | | [ k ] [ inf 2 ]> k = 0 [ q 1 ] [ ==== n n - n ]> [ \ a q ]> [ 0 > -------------- ]> [ / qpoch(q, q, n) ]> [ ==== ]> [ n = 0 ]> > (c45) TAYLOR(PRUD(PART(%,1,1),K,0,7) = MAKEPROD(RHS(%)),Q,0,6);>

[GARBLED] Isn't an eavesdropper a stoolpigeon? John