22 Feb
2012
22 Feb
'12
12:42 a.m.
* Bill Gosper <billgosper@gmail.com> [Feb 22. 2012 07:07]:
joerg>
* Bill Gosper <billgosper@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> [Feb 18. 2012 07:42]:> [...]
which is somewhat less peculiar when properly simplified:> > Sum[t^n/QPochhammer[x, q, 1 + n], {n, 0, Infinity}] ==> Sum[(q^j*QPochhammer[q^(1 + j), q])/(QPochhammer[q^j*t, q]*> QPochhammer[q^j*x, q]), {j, 0, Infinity}]> DLMF 17.6.12 http://dlmf.nist.gov/17.6
That's just Rogers-Fine. I'd like to find \[ % sum(n=0,N, t^n / qbin(x,q,n+1) ) % sum(n=0,N, x^n / qbin(t,q,n+1) ) \sum_{n\geq{}0}{ \frac{t^n}{(x;q)_{n+1}} } = \sum_{n\geq{}0}{ \frac{x^n}{(t;q)_{n+1}} } \]
--rwg
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