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 Tommy's Gamma trick ? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 10/22/2015, 12:34 PM (This post was last modified: 11/02/2015, 01:27 AM by tommy1729.) Let f be continu and real and satisfy : For x = Y $f(1) = 1$ (1) $f ' (x) = \Pi_1^Y f(x)$ (2) $f(2) = e$ For real $1 < Y < 2$ 1) does that imply f is C^oo in $x E [1,Y]$ ? 2) does that imply f is analytic in $[1,Y]$ ? 3) is the solution Unique ? If not, how many variables are there ? 4) how to prove existance ? 5) does it follow $f ' (2x) = \Pi_1^{2Y} f(x)$ ? 6) is the equation $f ' (x) = exp[ \Sigma 1^Y f(x-1) ]$ equivalent ? 7) does it Neccessarily follow $f(x+1) = exp {f(x)}$ for x>1 ? 8 ) If f is analytic on $[1,Y]$ does that imply it is analytic in $[2,1+Y]$ ? Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Tommy's Gamma trick ? - by tommy1729 - 10/14/2015, 09:37 PM RE: Tommy's Gamma trick ? - by tommy1729 - 10/16/2015, 12:28 PM RE: Tommy's Gamma trick ? - by tommy1729 - 10/17/2015, 12:22 AM RE: Tommy's Gamma trick ? - by tommy1729 - 10/22/2015, 12:34 PM RE: Tommy's Gamma trick ? - by tommy1729 - 11/02/2015, 01:43 AM RE: Tommy's Gamma trick ? - by tommy1729 - 11/04/2015, 12:06 AM RE: Tommy's Gamma trick ? - by tommy1729 - 11/04/2015, 01:26 PM RE: Tommy's Gamma trick ? - by tommy1729 - 11/07/2015, 01:02 PM

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