Lit: f(x)=log(x) iff x is integer
#1
You may like the article of Ed Sandifer about a series, which interpolates the logarithm at integers, but not at non-integers. The form of the series has also some in common with the series for U(x) = exp(x)-1 by my eigensystem-decomposition, so there may be some additional interest.

See Sandifer_HowEulerDidIt_dec2007

Have fun -

Gottfried
Gottfried Helms, Kassel
#2
Page is no longer available.
I do not like the idea that Ed's musings are removed from the (free) internet.
Im not even sure we would have liked that.

Seems the world has a love/hate affair with " for free " which I do not like at all.

regards

tommy1729
#3
(03/16/2015, 11:38 PM)tommy1729 Wrote: Page is no longer available.
I do not like the idea that Ed's musings are removed from the (free) internet.
Im not even sure we would have liked that.

Seems the world has a love/hate affair with " for free " which I do not like at all.

regards

tommy1729

Just foud the reorganized links; they reside now under ams.hedi.<something>. The dec 2007 ("False logarithmic series") is at
http://eulerarchive.maa.org/hedi/HEDI-2007-12.pdf

Gottfried
Gottfried Helms, Kassel
#4
Thank you !

I want to say that 1729 in my pseudo does not only refer to the taxicab number but also to the time when Euler and Goldbach communicated with each other and wrote intresting things.

Euler inspired me.
The link is more important for others then for me, because I know the papers of euler almost by heart.

regards

tommy1729


Possibly Related Threads…
Thread Author Replies Views Last Post
  Frozen digits in any integer tetration marcokrt 2 1,123 08/14/2022, 04:51 AM
Last Post: JmsNxn
Question Closed Forms for non Integer Tetration Catullus 1 886 07/08/2022, 11:32 AM
Last Post: JmsNxn
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 6,154 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Tetration series for integer exponent. Can you find the pattern? marraco 20 39,854 02/21/2016, 03:27 PM
Last Post: marraco
  Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers tommy1729 0 4,676 08/17/2014, 09:01 PM
Last Post: tommy1729
  Integer tetration and convergence speed rules marcokrt 5 15,223 12/21/2011, 06:21 PM
Last Post: marcokrt
  2 [n] b and 3 [n] b for (large) integer n, b dyitto 2 7,828 03/12/2011, 10:52 PM
Last Post: dyitto
  Observations on branching and integer iterates jaydfox 1 6,936 11/23/2007, 08:31 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)