Nice. Could you supply an non-garbled version (image?) of the things below (c45)? 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> [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]