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 Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... tommy1729 Ultimate Fellow     Posts: 1,370 Threads: 335 Joined: Feb 2009 03/13/2013, 10:52 PM Another trivial proof. Lets start with demystifying where the constant comes from. exp(x)/M = x * f(x) * f^(x)*... It was already shown that f was x - ln(x). As usual we search for fixpoints. 1 is a fixpoint of x - ln(x) since 1 - ln(1) = 1. We also know that f^[n](x) must approach 1 in the limit. Hence if we plug in x=1 on the RHS we get 1 * 1 * 1 * ... = 1 Therefore we get exp(x)/M = 1 => exp(1)/M = 1 => e/M = 1 => M = e Q.E.D. This thread reminds me a bit of an idea I had not so long ago http://math.eretrandre.org/tetrationforu...hp?tid=768 Im not sure where you want to go next with this. Like how to build tetration from it , or other intresting properties. Afterall we know it is analytic. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by Gottfried - 03/12/2013, 08:58 AM RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by Balarka Sen - 03/12/2013, 10:01 AM RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by Gottfried - 03/12/2013, 10:13 AM RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by tommy1729 - 03/13/2013, 12:12 AM RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by tommy1729 - 03/13/2013, 10:52 PM RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by Gottfried - 07/17/2013, 09:46 AM

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