an intrigeing beauty (by Srinivasa R.) is 1/(1+ContinuedFractionK[n+1,1,{n,0,inf}])==Sqrt[E Pi/2]-Sum[1/(2n-1)!!,{n,1,inf}] does Mathematica 8.0 "know" of this? Wouter. ----- Original Message ----- From: "Bill Gosper" <billgosper@gmail.com> To: <math-fun@mailman.xmission.com> Sent: Thursday, December 01, 2011 7:59 PM Subject: Re: [math-fun] Convolution and continued fractions
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
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