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 Status of proofs bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/27/2007, 08:54 AM So it indeed seems that Gottfried's method also leads to the same result as Andrew's approach. So I add to the list of lacking proofs Let $E_b$ be the power derivation matrix of $x\to b^x$ at 0, show that $E_b^t := \sum_{n=0}^\infty \left(t\\n\right) (E_b-I)^n$ exists (for each $b>1$ and each mxm truncation of $E_b$) and that the first row are the coefficients of a powerseries $e_b^t$ such that $\text{slog}_b(e_b^t(1))=t$ for Andrew's slog. An easier step into that direction could be to show that $e_b^t(x)$ is equal to the regular iteration at the lower fixed point of $b^x$ for $1. « Next Oldest | Next Newest »

 Messages In This Thread Status of proofs - by Daniel - 08/24/2007, 06:56 PM RE: Status of proofs - by bo198214 - 08/24/2007, 07:16 PM RE: Status of proofs - by bo198214 - 08/24/2007, 07:23 PM RE: Status of proofs - by Daniel - 08/24/2007, 11:09 PM RE: Status of proofs - by bo198214 - 08/25/2007, 12:07 AM RE: Status of proofs - by bo198214 - 08/27/2007, 08:54 AM RE: Status of proofs - by Gottfried - 08/24/2007, 10:06 PM RE: Status of proofs - by Daniel - 08/24/2007, 11:02 PM RE: Status of proofs - by Gottfried - 08/29/2007, 06:07 AM RE: Status of proofs - by andydude - 08/29/2007, 05:04 AM RE: Status of proofs - by tommy1729 - 07/20/2010, 10:02 PM RE: Status of proofs - by bo198214 - 07/21/2010, 03:08 AM RE: Status of proofs - by tommy1729 - 07/21/2010, 10:39 PM

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