Great! I'd love to see the rest of the slides. I take it the denominator in each sum is the generalized q-Pochhammer symbol described at the bottom of the page here: http://mathworld.wolfram.com/q-PochhammerSymbol.html On Thu, Dec 8, 2011 at 5:46 AM, Bill Gosper <billgosper@gmail.com> wrote:
I just stumbled upon slides from some forgotten talk containing a matrix sketch of an identity which specializes to 2 n inf 2 -- - n/2 ==== n n 2 \ (- 1) %i q (c + %i) > --------------------- / n %i ==== c (- --, - q; - q) n = 0 c n ------------------------------------ 2 n inf 2 -- + n/2 ==== n 2 \ %i q > -------------------- / n %i q ==== c (- q, ----; - q) n = 0 c n
= 1 c + ----------------- c 1 - + ------------- q c 1 -- + -------- 2 c 1 q -- + --- 3 . q . .
(Sorry, no Mma. It was being unusably, inconceivably stupid on this.) --rwg
On Thu, Dec 1, 2011 at 10:59 AM, Bill Gosper <billgosper@gmail.com> wrote:
On Wed, Nov 30, 2011 at 2:51 PM, Bill Gosper <billgosper@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> wrote:> This promised to be quite tedious, except that it was possible to take "unconscionable> shortcuts" (I think I called them). I think I can dig up some results, if you want.
Yes, please; I don't get any hits on searching my archive for "unconscionable" except this email. -- Mike Stay - metaweta@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=metaweta%40gmail.com>http://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
You can pretty much find everything searching for ContinuedFractionK. But I see a big garble in a msg containing [...] And constant/linear gives 1F0
ContinuedFractionK[e, a n + b, {n, 1, Infinity}] ==
b e e Hypergeometric0F1[2 + -, --] a 2 a ------------------------------------, b e (a + b) Hypergeometric0F1[1 + -, --] a 2 a and a pattern emerges. But not quite.[...] ------------- The pattern in question predicted the values of p and q in the pFqs based on the degrees of the two polynomials in the ContinuedFractionK, to which I'd found a strange exception. Unfortunately, I seem to have spazzed the editing and stated the same example twice in succession. --rwg I think the aforementioned shortcuts somehow combined the determination of the ODE integration constants with the subsequent limit-taking.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com