Re: [math-fun] tiny 2x2 simultaneously computes both Rogers-Ramanujan sums

10 Oct 2012


      * meg <njasloane@gmail.com> [Oct 09. 2012 07:01]:
...
Joerg, Yes, certainly! Thank you!
Neil
[...]
Now in  https://oeis.org/draft/A003106 :
...
From _Joerg Arndt_, Oct 10 2012: (Start)
R. W. Gosper gives (message to the math-fun mailing list, Oct 07 2012)
prod(k>=0, [0 , a;  q^k, 1]) = [0, X(a,q);  0, Y(a,q)] where
X(a,q) = a * sum(n>=0, a^n*q^(n^2) / prod(k=1..n, 1-q^n) ) and
Y(a,q) = sum(n>=0, a^n*q^(n^2-n) / prod(k=1..n, 1-q^n) ).
Set a=q to obtain
prod(k>=0, [0 , a;  q^k, 1]) = [0, q*H(q);  0, G(q)] where
H(q) is the g.f. of A003106 and G(q) is the g.f. of A003114.
(End)
I will now look at the following message.

Regards,   jj