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

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

(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

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