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.